{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# From Ordinary Differential equations to Neural Networks, solving mechanics problems in a new way" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Harmonic Oscillations\n", "\n", "Harmonic oscillations are a fundamental concept in physics and engineering that describe the repetitive motion of a system around an equilibrium position. A harmonic oscillator can be found in many physical systems, such as pendulums, springs, and electrical circuits. These systems can be modeled mathematically as a simple harmonic motion, which is characterized by a sinusoidal displacement with a constant amplitude and frequency. The understanding of harmonic oscillations is essential for various fields, including mechanics, electromagnetism, and quantum mechanics. In this context, the study of harmonic oscillations provides insights into the behavior of physical systems and their response to external stimuli, allowing us to design and optimize devices and structures for various applications.\n", "\n", "## Harmonic Oscillator: Spring-Block System" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\nonumber\n", "F=-\\frac{dV(x)}{dx}=-k(x-b).\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our equation of motion is, with the only force given by the one-dimensional spring force and assuming $b=0$, " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "ma = m\\frac{d^2x}{dt^2}=-kx.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Defining the natural frequency $\\omega_0 = \\sqrt{k/m}$, we can rewrite this equation as" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{dt^2}=-\\omega_0^2x.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We call this a natural frequency since it is defined by the constants that describe our system, the spring constant $k$ and the mass $m$ of the object.\n", "\n", "The dimensionality of $\\omega_0$ is $[T]^{-1}$.\n", "\n", "We can as usual split this equation of motion into one equation for the derivative of the velocity and" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{dv}{dt}=-\\omega_0^2x,\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{dx}{dt}=v.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution to the equations of motion is given by" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "x(t) = A\\cos{(\\omega_0 t)}+B\\sin{(\\omega_0 t)},\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "where $A$ and $B$ are in general complex constants to be determined by the initial conditions.\n", "\n", "Inserting the solution into the equation of motion, we have:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{dt^2}=-\\omega_0^2x,\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "we have" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{dt^2} = -A\\omega_0^2\\cos{(\\omega_0 t)}-B\\omega_0^2\\sin{(\\omega_0 t)},\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and the right-hand side is just $-\\omega_0^2 x(t)$. Thus, inserting the solution into the differential equation shows that we obtain the same original differential equation.\n", "\n", "\n", "\n", "Let us assume that our initial time $t_0=0$s and that the initial position $x(t_0)=x_0$ and that $v_0=0$ (we skip units here).\n", "This gives us" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "x(t=0) = x_0 =A,\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and it leaves $B$ undetermined. Taking the derivative of $x$, we obtain the velocity:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "v(t) = -A\\omega_0\\sin{(\\omega_0 t)}+B\\omega_0\\cos{(\\omega_0 t)},\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and with" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "v(t=0) = 0=B,\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "we see that our solution with these initial conditions becomes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "x(t) = x_0\\cos{(\\omega_0 t)}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Energy Conservation\n", "\n", "Our energy is given by the kinetic energy and the harmonic oscillator potential energy, that is we have (for a one-dimensional harmonic oscillator potential)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "E=\\frac{1}{2}mv^2+\\frac{1}{2}kx^2.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We assume that we have initial conditions $v_0=0$ (no kinetic energy) and $x(t=0)=x_0$.\n", "With these initial conditions we have" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "x(t) = x_0\\cos{(\\omega_0 t)},\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and the velocity is given by" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "v(t) = -x_0\\omega_0\\sin{(\\omega_0 t)},\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At a time $t\\ne 0$, we have:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "E(t)=\\frac{1}{2}mv^2+\\frac{1}{2}kx^2=\\frac{1}{2}mx_0^2\\omega_0^2\\sin^2{(\\omega_0 t)}+\\frac{1}{2}kx_0^2\\cos^2{(\\omega_0 t)},\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recalling that $\\omega_0^2=k/m$, we get:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "E(t)=\\frac{1}{2}kx_0^2\\sin^2{(\\omega_0 t)}+\\frac{1}{2}kx_0^2\\cos^2{(\\omega_0 t)}=\\frac{1}{2}kx_0^2=E_0.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For $x_0 = A$,\n", "\n", "$$E_0 = \\frac{1}{2}kx_0^2 = \\frac{1}{2}kA^2$$\n", "\n", "Energy is thus conserved." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Scaling with $\\tau = \\omega_0t$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{dt^2}=-\\omega_0^2x => \\omega_0^2\\frac{d^2x}{d\\tau^2}=-\\omega_0^2x,\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dividing by $\\omega_0^2$ on both sides, we get:\n", "\n", "$$a = \\frac{d^2x}{d\\tau^2}= \\frac{dv}{d\\tau} = -x$$\n", "\n", "Now, the dimensionality of both $\\frac{dv}{d\\tau} = -x$ and $\\frac{dx}{d\\tau} = v$ is $[L]$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution to this is given by:\n", "\n", "$$x(\\tau) = x_0\\cos{(\\tau)}, v(\\tau) = -x_0\\sin{(\\tau)}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Euler-Cromer" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from math import *\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "DeltaT = 0.01\n", "#set up arrays \n", "tfinal = 20 # in seconds\n", "n = ceil(tfinal/DeltaT)\n", "# set up arrays for t, a, v, and x\n", "t = np.zeros(n)\n", "v = np.zeros(n)\n", "x = np.zeros(n)\n", "# Initial conditions as compact 2-dimensional arrays\n", "x0 = 2\n", "v0 = 0\n", "x[0] = x0\n", "v[0] = v0\n", "# Start integrating using Euler's method\n", "for i in range(n-1):\n", " # Set up the acceleration\n", " a = -x[i]\n", " # update velocity, time and position using Euler's forward method\n", " v[i+1] = v[i] + DeltaT*a\n", " x[i+1] = x[i] + DeltaT*v[i+1]\n", " t[i+1] = t[i] + DeltaT\n", "m = 1\n", "k = 1\n", "K = 1/2*m*v**2\n", "V = 1/2*k*x**2\n", "E = K+V\n", "# Plot position, velocity and total energy as function of time \n", "fig, ax = plt.subplots(3,1)\n", "fig.set_size_inches(15,10)\n", "ax[0].set_title('Euler-Cromer')\n", "ax[0].plot(t,x)\n", "ax[1].plot(t,v)\n", "ax[2].plot(t,E)\n", "ax[2].set_ylim([0,20])\n", "ax[2].set_xlabel('Time (s)')\n", "ax[0].set_ylabel('Position (m)')\n", "ax[1].set_ylabel('Velocity (m/s)')\n", "ax[2].set_ylabel('Energy (J)')\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Velocity-Verlet" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "DeltaT = 0.01\n", "#set up arrays \n", "tfinal = 20\n", "n = ceil(tfinal/DeltaT)\n", "# set up arrays for t, a, v, and x\n", "t = np.zeros(n)\n", "v = np.zeros(n)\n", "x = np.zeros(n)\n", "# Initial conditions as compact 2-dimensional arrays\n", "x0 = 2\n", "v0 = 0\n", "x[0] = x0\n", "v[0] = v0\n", "# Start integrating using the Velocity-Verlet method\n", "for i in range(n-1):\n", " # Set up the acceleration\n", " a = -x[i]\n", " # update velocity, time and position using the Velocity-Verlet method\n", " x[i+1] = x[i] + DeltaT*v[i]+0.5*(DeltaT**2)*a\n", " anew = -x[i+1]\n", " v[i+1] = v[i] + 0.5*DeltaT*(a+anew)\n", " t[i+1] = t[i] + DeltaT\n", "m = 1\n", "k = 1\n", "K = 1/2*m*v**2\n", "V = 1/2*k*x**2\n", "E = K+V\n", "# Plot position, velocity and total energy as function of time \n", "fig, ax = plt.subplots(3,1)\n", "fig.set_size_inches(15,10)\n", "ax[0].set_title('Velocity-Verlet')\n", "ax[0].plot(t,x)\n", "ax[1].plot(t,v)\n", "ax[2].plot(t,E)\n", "ax[2].set_ylim([1.5,2.5])\n", "ax[2].set_xlabel('Time (s)')\n", "ax[0].set_ylabel('Position (m)')\n", "ax[1].set_ylabel('Velocity (m/s)')\n", "ax[2].set_ylabel('Energy (J)')\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The velocity Verlet method is generally considered to be a better method than the Euler-Cromer method when it comes to simulating systems with energy conserving forces.\n", "\n", "The Euler-Cromer method is a simple and widely used numerical integration method that updates the position and velocity of a system sequentially, with the velocity being updated using the new position. While this method is easy to implement, it is known to produce errors that accumulate over time, leading to a loss of accuracy and energy conservation in the simulation.\n", "\n", "On the other hand, the velocity Verlet method is a more accurate numerical integration method that updates both the position and velocity of a system simultaneously. This method is symplectic, meaning it conserves the energy of the system and is thus particularly useful for simulating systems with energy conserving forces. The velocity Verlet method is also more stable and accurate than the Euler-Cromer method, and it is widely used in molecular dynamics simulations, where energy conservation is critical.\n", "\n", "Overall, the velocity Verlet method is considered to be a better choice than the Euler-Cromer method when simulating systems with energy conserving forces, as it provides better accuracy and energy conservation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sliding Block (With Damping Due To Friction)\n", "\n", "Now, we change the differential equation we want to solve by adding to our program a first derivative of position (the velocity) which is meant to mimick the role of friction." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "m\\frac{d^2x(t)}{dt^2} + \\beta\\frac{dx}{dt}+kx = ma(t)+\\beta v(t) +kx(t) = 0.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We divide by $m$ and introduce $\\omega_0^2=\\sqrt{k/m}$ and obtain" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{dt^2} + \\frac{\\beta}{m}\\frac{dx}{dt}+\\omega_0^2x(t) =0.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thereafter, we introduce a dimensionless time $\\tau = t\\omega_0$ and rewrite our equation as:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{d\\tau^2} + \\frac{\\beta}{m\\omega_0}\\frac{dx}{d\\tau}+x(\\tau) =0,\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "which gives us" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{d\\tau^2} + \\frac{b}{m\\omega_0}\\frac{dx}{d\\tau}+x(\\tau) =0.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then define $\\gamma = b/(2m\\omega_0)$ and rewrite our equation as:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{d\\tau^2} + 2\\gamma\\frac{dx}{d\\tau}+x(\\tau) =0.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This gives us:\n", "\n", "$$\\frac{d^2x}{d\\tau^2} = - 2\\gamma v(t)-x(\\tau) \\text{ where } v(t) = \\frac{dx}{d\\tau}$$\n", "\n", "Again, the dimensionality of both $\\frac{dv}{d\\tau} = -2\\gamma v(t)-x(\\tau)$ and $\\frac{dx}{d\\tau} = v(t)$ is $[L]$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical Solutions of Damped Oscillations\n", "\n", "With $k=1, m=1$, it means $\\omega_0 = 1$. Thus, $\\gamma$ can be chosen accordingly for the three cases: underdamping, critical damping and overdamping.\n", "\n", "### (i) Underdamping" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "DeltaT = 0.01\n", "#set up arrays \n", "tfinal = 20 # in seconds\n", "n = ceil(tfinal/DeltaT)\n", "# set up arrays for t, a, v, and x\n", "t = np.zeros(n)\n", "v = np.zeros(n)\n", "x = np.zeros(n)\n", "# Initial conditions as compact 2-dimensional arrays\n", "x0 = 2\n", "v0 = 2\n", "x[0] = x0\n", "v[0] = v0\n", "gamma = 0.2\n", "# Start integrating using Euler's method\n", "for i in range(n-1):\n", " # Set up the acceleration\n", " a = -2*gamma*v[i]-x[i]\n", " # update velocity, time and position using Euler's forward method\n", " v[i+1] = v[i] + DeltaT*a\n", " x[i+1] = x[i] + DeltaT*v[i+1]\n", " t[i+1] = t[i] + DeltaT\n", "m = 1\n", "k = 1\n", "# Plot position and velocity as function of time \n", "fig, ax = plt.subplots(2,1)\n", "fig.set_size_inches(8,10)\n", "ax[0].set_title('Underdamping')\n", "ax[0].plot(t,x)\n", "ax[1].plot(t,v)\n", "ax[1].set_xlabel('Time (s)')\n", "ax[0].set_ylabel('Position (m)')\n", "ax[1].set_ylabel('Velocity (m/s)')\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (ii) Critical Damping" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "DeltaT = 0.01\n", "#set up arrays \n", "tfinal = 20 # in seconds\n", "n = ceil(tfinal/DeltaT)\n", "# set up arrays for t, a, v, and x\n", "t = np.zeros(n)\n", "v = np.zeros(n)\n", "x = np.zeros(n)\n", "# Initial conditions as compact 2-dimensional arrays\n", "x0 = 2\n", "v0 = 2\n", "x[0] = x0\n", "v[0] = v0\n", "gamma = 1\n", "# Start integrating using Euler's method\n", "for i in range(n-1):\n", " # Set up the acceleration\n", " a = -2*gamma*v[i]-x[i]\n", " # update velocity, time and position using Euler's forward method\n", " v[i+1] = v[i] + DeltaT*a\n", " x[i+1] = x[i] + DeltaT*v[i+1]\n", " t[i+1] = t[i] + DeltaT\n", "m = 1\n", "k = 1\n", "# Plot position and velocity as function of time \n", "fig, ax = plt.subplots(2,1)\n", "fig.set_size_inches(8,10)\n", "ax[0].set_title('Critical Damping')\n", "ax[0].plot(t,x)\n", "ax[1].plot(t,v)\n", "ax[1].set_xlabel('Time (s)')\n", "ax[0].set_ylabel('Position (m)')\n", "ax[1].set_ylabel('Velocity (m/s)')\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### (iii) Overdamping" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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MH1k6Tauq67Rq+0G/ywEAwFcEnCzy/oWTlR8L6/fPbfW7FAAAfEXAySLFuVG97/jJWr5qpw40tftdDgAAviHgZJmPLJ2mts647nqx2u9SAADwDQEnyxw1sVgnTB+j3z+/VfG487scAAB8QcDJQh9eOk1b9zXriQ21fpcCAIAvCDhZ6Jz5E1ReGGOyMQBg1CLgZKGcSFgfPKFSf3utRtv3N/tdDgAAI46Ak6U+vHSaQma65ZktfpcCAMCII+BkqYkleTrvmIm6c8V2NbZ1+l0OAAAjioCTxa46eboa2jp1V9V2v0sBAGBEEXCy2PFTx+i4ylLd/MwWThkHAIwqBJwsd9UpM7RlX7MeW1/jdykAAIwYAk6WO3f+BE0oztVNT2/2uxQAAEYMASfLRcMhffSkaXp64z69trve73IAABgRBJxR4PITpio3GtJvntridykAAIwIAs4oMKYgposWTtG9L+/QvsY2v8sBACDtCDijxMdPmq72zrhue36b36UAAJB2BJxRYs74Ip12RIVueXarWju6/C4HAIC0IuCMIv902kztbWzTvS/t8LsUAADSyteAY2Y3mVmNma3pY/vpZlZnZi97j2+NdI3Z5KRZYzV/crFueGITF/4DAGQ1v3twbpZ0zmHaPOmcO857fHcEaspaZqZ/Om2WNu1t0iPr9vhdDgAAaeNrwHHOPSFpv581jDbnzp+gyrI8/fIfb8g5enEAANnJ7x6cgVhmZqvM7AEzm+d3MZkuEg7pU6fO1EvbDqpq6wG/ywEAIC2CHnBWSprmnDtW0k8l3ddbIzO72syqzKyqtrZ2JOvLSJcuqtSY/Kh+9Y83/C4FAIC0CHTAcc7VO+caveX7JUXNrLyXdtc75xY75xZXVFSMeJ2ZJi8W1sdOmq5H19Vow54Gv8sBACDlAh1wzGyCmZm3vESJevf5W1V2+Oiy6cqNhnT9E5v8LgUAgJTz+zTx2yU9K2mumVWb2SfM7NNm9mmvySWS1pjZKkk/kXSZY2ZsSpQVxPTBxZW67+Ud2l3X6nc5AACkVMTPD3fOXX6Y7T+T9LMRKmfU+eSpM/X757fpxic36d/PP9rvcgAASJlAD1EhvSrL8nXhsZN06/PbuAknACCrEHBGuc++c5ZaO7t009Ob/S4FAICUIeCMcrPHFem8+RN1yzNbVdfc4Xc5AACkBAEH+vy7ZquxrVO3PLvF71IAAEgJAg501MRivfuo8brp6c1qbOv0uxwAAIaNgANJiV6cg80duvW5rX6XAgDAsBFwIEk6rrJUp84p1w1PblJrR5ff5QAAMCwEHBzyz++ao72N7brjhW1+lwIAwLAQcHDIkhllWjKjTL/8B704AIDMRsDBW3zpjDnaXd9KLw4AIKMRcPAWy2aN1YkzynTd42+opZ1eHABAZiLg4C3MTF8+a65qG9r0e86oAgBkqJTcbNPMFks6VdIkSS2S1kh6xDl3IBX7x8haMqNMp84p1y/+8YauOHGqCnJ8vScrAACDNqweHDP7uJmtlPQNSXmS1kuqkXSKpEfN7BYzmzr8MjHS/uXMI7S/qV03P7PF71IAABi04f6veb6kk51zLb1tNLPjJM2RxIzVDHP81DF615HjdP0Tm/SRZdNUnBv1uyQAAAZsWD04zrnr+go33vaXnXN/G85nwD//cuYRqmvp0E1PcadxAEBmSdUcnBmS/lnS9OR9OucuSMX+4Y/5k0t09rzx+vWTm3XlSdNVmh/zuyQAAAYkVWdR3Sdpi6SfSvrvpAcy3P935hFqbO/U9U9s8rsUAAAGLFWnx7Q6536Son0hQI6cUKz3Lpikm55O9OKMK871uyQAAA4rVT04Pzazb5vZMjNb2P1I0b7hs6+cNVddcacfPbrB71IAABiQVPXgHCPpI5LeJSnurXPea2S4qWPz9aETp+l3z23VJ06ZodnjCv0uCQCAfqWqB+dSSTOdc+9wzr3TexBussg/v2u28qJh/fCh9X6XAgDAYaUq4KyRVJqifSGAxhbm6OrTZurBtbu1chsXqAYABFuqAk6ppNfM7CEzW979SNG+ERCfOGWGygtz9L37X5Nzzu9yAADoU6rm4Hw7RftBgBXkRPTFd8/Rf9y3Rn9/rUZnHDXe75IAAOjVsAKOmZlL+Mfh2gzncxAcl51QqV8/uUnff/A1nT53nMIh87skAADeZrhDVI+Z2T/3vKGmmcXM7F1mdoukjw3zMxAg0XBIXz37SL2+p1F/rNrudzkAAPRquAHnHEldkm43s51m9qqZbZa0QdLlkv7XOXfzMD8DAXPeMRO0aNoY/fDh19XY1ul3OQAAvM1wb7bZ6pz7uXPuZEnTJJ0h6Xjn3DTn3Keccy+lpEoEipnpP84/Wnsb2/Tzxzb6XQ4AAG+TqrOo5JzrcM7tcs4dTNU+EVzHVZbqouMn68anNmv7/ma/ywEA4C1SFnAw+nz1nLkKmfS9B17zuxQAAN6CgIMhm1iSp0+/Y5b+unqXVmzZ73c5AAAcQsDBsFx92kxNKM7Vd//8quJxrgYAAAiGlAQcM7vIzDaYWZ2Z1ZtZg5nVp2LfCLb8WET/eu5crd5Rp3te2uF3OQAASEpdD861ki5wzpU454qdc0XOueIU7RsBd+Gxk3VsZamuffA1NbR2+F0OAAApCzh7nHPrUrQvZJhQyPSdC+aptrFNP/nbBr/LAQAgZfeiqjKzOyXdJ6mte6Vz7p4U7R8Bd1xlqS47oVI3Pb1Flyyq1NwJRX6XBAAYxVLVg1MsqVnSWZLe6z3OT9G+kSG+evaRKsqN6Ft/WsPdxgEAvkpJD45z7uOp2A8yW1lBTF87+0j9272rtXzVTl143GS/SwIAjFKpOotqipnda2Y13uNuM5uSin0js3zwhEodO6VE//nXdUw4BgD4JlVDVL+RtFzSJO/xZ28dRplwyPTdC+drb2Ob/vdRJhwDAPyRqoBT4Zz7jXOu03vcLKkiRftGhjm2slSXL5mqm5/Zotd2czkkAMDIS1XA2WdmHzazsPf4sKR9Kdo3MtBXz5qr4tyI/uO+NVzhGAAw4lIVcK6S9AFJuyXtknSJJCYej2JjCmL6xnlHacWWA7p9xTa/ywEAjDIpCTjOua3OuQuccxXOuXHOufc55/irNspdumiKTpo1Vt+7/zXtqW/1uxwAwCgyrIBjZl/znn9qZj/p+UhNichUZqb/+/5j1N4V1zXL1/pdDgBgFBnudXC6b89QNdxCkJ2mlxfoi++eo2sfXK+H1+7WWfMm+F0SAGAUGFbAcc792Vtsds79MXmbmV06nH0je3zq1Jla/vJOfetPa7Vs1lgV5Ub9LgkAkOVSNcn4GwNch1EoGg7pexcv0J6GVl374Hq/ywEAjALD6sExs3MlnSdpco85N8WSOoezb2SX4ypLdeVJ03XzM1v0vuMnadG0Mr9LAgBkseH24OxUYv5Nq6QXkx7LJZ09zH0jy3zlrLmaVJKnr931ilo7uvwuBwCQxYYVcJxzq5xzt0ia5Zy7Jelxj3PuQIpqRJYoyIno+xcv0Bu1TfqfR173uxwAQBYb7mnif/AWXzKzV5Ieq83slRTUhyxzypxyfejEqbrhyU2q2rLf73IAAFlquKeJf9F7Pn+4hWD0+MZ5R+kfr9fqK39cpQe+eJryYmG/SwIAZJnhDlHt8hb3StrunNsqKUfSsUrMz+mXmd1kZjVmtqaP7eZdNHCj1zO0cDj1IhgKcyL6wSXHasu+Zl370Gt+lwMAyEKpOk38CUm5ZjZZ0sOSPiLp5gG872ZJ5/Sz/VxJc7zH1ZJ+MawqERjLZo3VlSdN12+e3qLnNnFfVgBAaqUq4JhzrlnSRZJ+7py7VNK8w73JOfeEpP4mYlwo6bcu4TlJpWY2MSUVw3dfO2eupo3N11fvWqWmNq4qAABInZQFHDNbJulDkv7qrUvFxIrJkrYnva721vX88KvNrMrMqmpra1PwsRgJ+bGIfnjpsao+0KL//Ou6w78BAIABSlXA+ZISVy6+1zm31sxmSnosRfs+LOfc9c65xc65xRUVFSP1sUiBE6aX6Z9Om6XbX9imh9bu9rscAECWSEnAcc79wzl3gaTrzKzQObfJOfeFFOx6h6TKpNdTvHXIIv9y5hGaP7lYX7/7Fe2pb/W7HABAFkhJwDGzY8zsJUlrJb1qZi+a2WHn4AzAckkf9c6mWiqpLunMLWSJWCSkH192vFo6uvSVP65SPO78LgkAkOFSNUT1K0n/4pyb5pybKunLkm443JvM7HZJz0qaa2bVZvYJM/u0mX3aa3K/pE2SNnr7+2yK6kXAzKoo1LfOn6cnN+zVTU9v9rscAECGG+6F/roVOOcOzblxzj1uZgWHe5Nz7vLDbHeSPpeC+pABLl9SqcfW1+jaB9frpFnlOnpSsd8lAQAyVKp6cDaZ2X+Y2XTv8e9K9LwAA2Zm+v7FC1SSH9UX73iJG3ICAIYsVQHnKkkVku6RdLekcm8dMChlBTH996XHakNNo77z57V+lwMAyFDDGqIys1xJn5Y0W9JqSV92znWkojCMXqcdUaHPnD5Lv3j8DZ04Y6zed/zbLn0EAEC/htuDc4ukxUqEm3Ml/WDYFQGSvnzmETph+hj9272rtbGm0e9yAAAZZrgB52jn3Iedc7+SdImk01JQE6BIOKSfXr5QudGwPnfrSrW0Mx8HADBwww04h4ajnHPcTAgpNaEkVz/64HF6vaZB317e6w3nAQDo1XADzrFmVu89GiQt6F42s/pUFIjR7R1HVOhzp8/WH6qqdfeL1X6XAwDIEMOaZOycS8UNNYF+fendc7Riy379+31rNH9yieZOKPK7JABAwKXqNHEgbSLhkH5y+fEqzI3o6t9Vqa6ZE/UAAP0j4CAjjC/O1S8+tFA7D7boi3e+pC7uVwUA6AcBBxlj8fQyffu98/T4+lr96JHX/S4HABBgBBxklA+dOFUfXFypnz22UQ+u4cbyAIDeEXCQUcxM37lwno6tLNWX/7BKG/Y0+F0SACCACDjIOLnRsH714UXKi0V09e9eVF0Lk44BAG9FwEFGmlCSq59/aKGqDzTr87etVGdX3O+SAAABQsBBxloyo0z/9f5j9OSGvbrmz2vlHGdWAQAShnWhP8BvH1hcqTdqG/Wrf2zSrIpCffzkGX6XBAAIAAIOMt6/nn2kNtc26f/85VVNH1ugdx45zu+SAAA+Y4gKGS8UMv3vZcfpqInF+ufbX9Jru7kNGgCMdgQcZIX8WES//tgJKsgJ6xM3V6mmodXvkgAAPiLgIGtMKMnVrz92gvY3teuqm1eosa3T75IAAD4h4CCrzJ9cop9/aKHW7WrQZ37/oto7OX0cAEYjAg6yzjuPHKfvXZQ4ffxrd61SnBtzAsCow1lUyEqXLq5UTUObfvDQeo0vztU3zjvK75IAACOIgIOs9dnTZ2l3Xat+9cQmjSvO1SdO4Ro5ADBaEHCQtcxM11wwT7UNbfo/f3lV5YUxXXjcZL/LAgCMAObgIKuFvWvknDijTP/yh1V6eO1uv0sCAIwAAg6yXm40rF9feYLmTy7R5297SU9uqPW7JABAmhFwMCoU5kR0y8dP0MyKAn3qt1V6YfN+v0sCAKQRAQejRml+TL/7xImaVJKnq25eoVeqD/pdEgAgTQg4GFUqinJ066dOVGl+VB+96QXuWwUAWYqAg1FnYkmebv3kicqJhHTFDc8TcgAgCxFwMCpNG1ug2z+1VNGw6fLrn9OrOwk5AJBNCDgYtWZWFOrOq5cpNxrWFTc+p7U76/wuCQCQIgQcjGrTywt0x9VLlR8N64obnteaHYQcAMgGBByMetPGFuiOq5epMCeiK254TqurCTkAkOkIOICkqWPzdcfVS1WcF9UVNzynFVu4Tg4AZDICDuCpLMvXH/5pmSqKc/SRXz+vx16r8bskAMAQEXCAJJNK8/SHf1qmWRWF+tRvq7R81U6/SwIADAEBB+ihvDBHt1+9VAunjdEX73hJv39uq98lAQAGiYAD9KI4N6rfXrVE75o7Tv9+3xpd99hGOef8LgsAMEAEHKAPudGwfvmRRXrfcZP0g4fW6zt/flVdcUIOAGSCiN8FAEEWDYf0Px84TuWFObrxqc3aebBFP77seOXFwn6XBgDoBz04wGGEQqZ/P/9offu9R+uRdXt0+Q3PaW9jm99lAQD6QcABBujjJ8/QLz+8SOt21euinz+jTbWNfpcEAOgDAQcYhLPnTdDtVy9VY1unLvrFM1wQEAACioADDNLCqWN072dP0pj8mK644Tn9YcV2v0sCAPRAwAGGYNrYAt332ZO1dOZYfe3uV/SdP69VZ1fc77IAAB4CDjBEJflR/ebKE3TVyTP0m6e36OM3r1Bdc4ffZQEARMABhiUSDulb7z1a1168QM9t2qf3/fxpbaxh8jEA+I2AA6TAB06o1O2fWqqG1g69/7qn9dDa3X6XBACjGgEHSJHF08v0p8+fohkVBfqn372o//fAOublAIBPCDhACk0uzdMfP71MH146Vb/6xyZ96MbnVdPQ6ndZADDqEHCAFMuJhPWf7ztGP/rgsVpVfVDv+clTemEz18sBgJHka8Axs3PMbL2ZbTSzr/ey/UozqzWzl73HJ/2oExiK9x8/RX/63Ckqyono8hue0y8ef0NxbtYJACPCt4BjZmFJ10k6V9LRki43s6N7aXqnc+4473HjiBYJDNPcCUX60+dP1jnzJuj7D76mj970gmrqGbICgHTzswdniaSNzrlNzrl2SXdIutDHeoC0KMqN6mdXHK/vXXSMXtx6QOf8+En9bd0ev8sCgKzmZ8CZLCn5GvfV3rqeLjazV8zsLjOr7G1HZna1mVWZWVVtbW06agWGxcx02ZKp+vM/n6IJxbn6xC1Vumb5WrV2dPldGgBkpaBPMv6zpOnOuQWSHpF0S2+NnHPXO+cWO+cWV1RUjGiBwGDMHleoez93kq46eYZufmaL3nfd01q/u8HvsgAg6/gZcHZISu6RmeKtO8Q5t8851+a9vFHSohGqDUibnEhY33rv0frNlSdob2Ob3vvTp3TdYxu5Zg4ApJCfAWeFpDlmNsPMYpIuk7Q8uYGZTUx6eYGkdSNYH5BW7zxynB760ml699Hj9IOH1uuSXz7LbR4AIEV8CzjOuU5Jn5f0kBLB5Q/OubVm9l0zu8Br9gUzW2tmqyR9QdKV/lQLpMfYwhxdd8VC/eTy47VlX5Pe85MndeOTm9TF6eQAMCzmXHb9Q7p48WJXVVXldxnAoNU0tOrf7lmtR9fV6ITpY/S9ixdoVkWh32UBQKCZ2YvOucU91wd9kjEwaowrytUNH12s/770WK3f3aBz//dJ/fjRDWrr5EwrABgsAg4QIGamixdN0aNffofOmjdeP3r0db3nJ09pxRZu9QAAg0HAAQJoXFGufnbFQv3myhPU0t6lS3/5rL5xz2rVNXf4XRoAZAQCDhBg7zxynB75l9P0qVNn6M4V23TG//xD96ys5p5WAHAYBBwg4PJjEX3zPUdr+edP0eTSXP3LH1bpkl8+ozU76vwuDQACi4ADZIj5k0t072dP1rWXLNC2/c1678+e0jfuWa19jW2HfzMAjDIEHCCDhEKmDyyu1N+/crquOnmG/li1Xe/84eO6+enNXAkZAJIQcIAMVJwb1X+cf7Qe+OKpWjClVNf8+VWd/b9P6JFX9yjbrm0FAENBwAEy2JzxRfrdJ5bo+o8skpP0qd9W6YO/ek4vbTvgd2kA4CsCDpDhzExnzZugh790mv7r/fO1aW+T3v/zZ/S5W1dqy94mv8sDAF9wqwYgyzS1der6Jzbphic3qb0zrsuXTNXn3jlbE0py/S4NAFKur1s1EHCALFXT0KofP7pBd67YrlDI9KETp+ozp8/SuCKCDoDsQcABRqnt+5v1079v0N0rdygaNn1k6TT90ztmqbwwx+/SAGDYCDjAKLdlb5N+8vcNuu+lHcqJhPWxk6brk6fOIOgAyGgEHACSpDdqG/WTv23Q8lU7FQuH9METKvWpU2eqsizf79IAYNAIOADe4o3aRl3/j02656VqxZ303gUT9ZnTZ2vuhCK/SwOAASPgAOjVrroW/frJzbrthW1qbu/SGUeO02dOn6VF08bIzPwuDwD6RcAB0K8DTe367bNbdfMzm3WguUMLppToqpNn6LxjJioW4ZJZAIKJgANgQJrbO3X3i9X6zTNbtKm2SeOKcvThpdN0xYlTmZAMIHAIOAAGJR53emJDrW56eoueeL1WsUhIFx47SVeePF3zJpX4XR4ASOo74ET8KAZA8IVCptPnjtPpc8dpY02Dbn5mi+5+cYf++GK1jq0s1YeWTNX5x05Ufox/RgAEDz04AAasrrlDd62s1u0vbNPGmkYV5UT0vuMn64oTp+qoicV+lwdgFGKICkDKOOe0YssB3f7CNv119S61d8Z1/NRSXb5kqs47ZqIKc+jVATAyCDgA0uJAU7vueWmHbnt+q96obVJeNKxz5k/QxQunaNmssQqHONUcQPoQcACklXNOK7cd0N0rd+jPq3aqobVTE0ty9b7jJ+vihZM1exwXEASQegQcACOmtaNLf1tXo3tWVuvx12vVFXdaMKVEFxw7Se9ZMFETS/L8LhFAliDgAPBFbUOblq/aqXtWVmvtznpJ0uJpY3T+gok675iJGlec63OFADIZAQeA7zbVNur+1bv0l1d26bXdDTKTlkwv0/kLJuqc+RNVUcSFBAEMDgEHQKBsrGnQX15JhJ2NNY0ykxZNHaMzjx6vM48er5kVhX6XCCADEHAABNbrexr011d26ZFX9+jVXYlhrFkVBTrz6Ak68+jxOr6yVCHOxgLQCwIOgIxQfaBZf1tXo0de3aPnNu1TZ9ypvDCmM44cr3ceWaGTZperODfqd5kAAoKAAyDj1LV06PH1ibDzj/W1amjrVDhkWjR1jE47olzvOGKc5k0qpncHGMUIOAAyWkdXXC9tO6h/vF6jJ17fq9U76iRJYwtiOu2ICr3jiAqdNHusxhVxVhYwmhBwAGSV2oY2PbWxVv9YX6snNuzV/qZ2SdLscYVaNnOsls0aq6Uzx6qsIOZzpQDSiYADIGvF405rdtbpmTf26dk39mnFlv1qbu+SJB05oUhLuwPPjLEqyWf+DpBNCDgARo2Orrheqa7Tc5sSgadq6361dsRlJs0dX6SF08Zo8bQxWjRtjKaW5cuMOTxApiLgABi12jq7tGp7IvBUbT2gl7YeUENbpySpvDBHi6aVavG0Mi2cNkbzJxcrJxL2uWIAA9VXwIn4UQwAjKScSFhLZpRpyYwySVJX3GlDTYOqthzQyq0HVLX1gB5au0eSFIuENH9SsRZMKdWCKSVaMKVEM8sLOVMLyDD04ACApJr6Vq3cdkBVWw5oVfVBrdlRr5aOxDyewpyI5k0q1rGVpTpmcomOnVKqyrI8hraAAGCICgAGoSvutLGmUa9UH9Qr1XV6ZUed1u2sV3tXXJJUmh/VUROKddTEYh01sUhHTSzWnPGFDG8BI4whKgAYhHDINHdCkeZOKNKliyslSe2dcb2+p0Grqg9qdXWd1u2q120vbFVrRyL0REKmWRWFOtILPN3hp6Iwh94eYIQRcABggGKRkOZPLtH8ySXSiYl1XXGnzXub9Nrueq3bVa91uxr0wub9+tPLOw+9b0x+VLPHFWr2uCLNHleoOeMKNXtcoSaW5BJ8gDQh4ADAMIRD5oWXQp2/YNKh9Qea2vXa7gat21WvDTUN2ljTqAfW7NLB5o5DbQpzIppVUfCW4DOjokCVY/IVi4T8OBwgaxBwACANxhTEtGxW4gKD3Zxz2tfUro01jdpQ06g3ahq1saZRT22s1d0rqw+1C5k0eUyepo8t0LSx+Zo+tiDxKC9QZVke83yAASDgAMAIMTOVF+aovDBHS2eOfcu2+tYObaxp1NZ9Tdq8t1lb9zVpy94mLX95p+pbO5P2IU0qydOM8gJNHZuvKWPyNGWM91yap/LCHE5pB0TAAYBAKM6NauHUMVo4dczbth1sbtfmvU3auq9ZW7zgs2Vfsx5YvUsHkoa8pMQ8ocmleV7wyfOWEwFo8pg8VRTmKBJm+AvZj4ADAAFXmh/T8VNjOr6X8NPU1qkdB1u040CLqg80q/pAS+JxsEWPvLpHexvb39I+ZFJFUY4mlORpQnGOJpbkaXxxriaU5GhCcZ4mlORqQnGu8mIMgyGzEXAAIIMV5ER0xPgiHTG+qNftLe1d2nHwzeCzp75Vu+patae+VW/UNumZjfsO3bYiWUleVBOKczWhJFcVRTmqKMrxhtdiidfeUFtpfpQzwRBIBBwAyGJ5sbB3llbvAUiSGts6tdsLPbsOPbdod12b9tS3av3uBu1tbFNn/O0Xho2GTWMLclReFDsUesq9ADS2MKaygpjG5Mc0piCmsvwYPUMYMQQcABjlCnMih05170s87lTX0qG9jW2qbWhTbWOb9ja2q7ahTXsbE4+ahja9uqte+xrbew1DkpQTCamsIKbS/JjKCqKJ8HMoAEU1xgtEZQUxleRFVZwbVVFuhInTGDQCDgDgsEIhS4SPgpjm9DEc1i0edzrY0qH9TW060Nyh/U3tOtDUrgPNHTrQ3K79Te066D3vOliv/c3tqmvpUF93DjJLhLDi3KiK86IqyXtzuTg3mghCb1kXUUl+YlthbkQFsYjCBKRRh4ADAEipUMhUVpDohRmoLq+HqDv87GtqV31Lh+pbO1XX0uEte88tndq2v1n1LR2qa+lQU3vXYfefHwurICeiQu9RkBP2npPXdb8OqzAn+rY2BTkR5UXDyo2GmHeUAQg4AADfhYcQirp1dsXV0Nqp+tYOLwy9udzY2qmGtk41eY/GQ8td2nGw9S3r2zrjA/7MvGhYebHwoef8WFi50cTr/KT1h55jb27LjYaVH4t420LKiYSVE/GeoyHlRELKjYYVC4cYmhsGXwOOmZ0j6ceSwpJudM59r8f2HEm/lbRI0j5JH3TObRnpOgEAwRUJhw4Nnw1HR1dczW1damjrUFNbV1IYSgSg5vYutXR0qbm9S60dXWpu71RLe1wtHZ1q8bYdbG7XrrrkNon1fQ2/HU4snAg8ieCTCEKxSEg50e5Q9NZg1N0mN5rUNhJSNNz9MMUiIUVCieVoJKRY0rZoOPGeQ227t0VCioQso0KXbwHHzMKSrpN0pqRqSSvMbLlz7tWkZp+QdMA5N9vMLpP0fUkfHPlqAQDZLhoOqSQ/pJL8aEr365xTW2dcLe1dau7oSoQhL/i0dHSpraNLbZ1x79Glto6k5c649zqpzaH2iRC2r7G9j+0D75EajHDI3gxDhwJQ4nU0FFIkbIqEQ4qGTBGv3bffO6/fSezp4GcPzhJJG51zmyTJzO6QdKGk5IBzoaRrvOW7JP3MzMy5oWZhAABGlpkpN5oYmnr7pRrTpztYdcadOjrj6uiKq70rro4ul1j21h163RX32iW99tZ1xp233XnvSd7+Zvv27s/riquzy6kzHldrR6ekkf+z7WfAmSxpe9Lrakkn9tXGOddpZnWSxkraOyIVAgCQobqDlSQpx99a/JAVNyQxs6vNrMrMqmpra/0uBwAA+MzPgLNDUmXS6yneul7bmFlEUokSk43fwjl3vXNusXNucUVFRZrKBQAAmcLPgLNC0hwzm2FmMUmXSVreo81ySR/zli+R9Hfm3wAAgMPxbQ6ON6fm85IeUuI08Zucc2vN7LuSqpxzyyX9WtLvzGyjpP1KhCAAAIB++XodHOfc/ZLu77HuW0nLrZIuHem6AABAZsuKScYAAADJCDgAACDrEHAAAEDWIeAAAICsQ8ABAABZh4ADAACyDgEHAABkHcu2CwObWa2krWn8iHJl/80+R8MxShxntuE4swvHmV3SeZzTnHNvu09T1gWcdDOzKufcYr/rSKfRcIwSx5ltOM7swnFmFz+OkyEqAACQdQg4AAAg6xBwBu96vwsYAaPhGCWOM9twnNmF48wuI36czMEBAABZhx4cAACQdQg4AAAg6xBwemFm55jZejPbaGZf72V7jpnd6W1/3sym+1DmsJhZpZk9ZmavmtlaM/tiL21ON7M6M3vZe3zLj1qHy8y2mNlq7xiqetluZvYT7/t8xcwW+lHncJjZ3KTv6WUzqzezL/Vok5Hfp5ndZGY1ZrYmaV2ZmT1iZhu85zF9vPdjXpsNZvaxkat68Po4zh+Y2Wvez+W9Zlbax3v7/RkPkj6O8xoz25H0s3leH+/t99/mIOnjOO9MOsYtZvZyH+/NiO+zr78jgfn9dM7xSHpICkt6Q9JMSTFJqyQd3aPNZyX90lu+TNKdftc9hOOcKGmht1wk6fVejvN0SX/xu9YUHOsWSeX9bD9P0gOSTNJSSc/7XfMwjzcsabcSF7/K+O9T0mmSFkpak7TuWklf95a/Lun7vbyvTNIm73mMtzzG7+MZ5HGeJSniLX+/t+P0tvX7Mx6kRx/HeY2krxzmfYf9tzlIj96Os8f2/5b0rUz+Pvv6OxKU3096cN5uiaSNzrlNzrl2SXdIurBHmwsl3eIt3yXpDDOzEaxx2Jxzu5xzK73lBknrJE32tyrfXCjpty7hOUmlZjbR76KG4QxJbzjn0nlF7xHjnHtC0v4eq5N/B2+R9L5e3nq2pEecc/udcwckPSLpnHTVOVy9Hadz7mHnXKf38jlJU0a8sBTr4/sciIH82xwY/R2n9/fiA5JuH9GiUqyfvyOB+P0k4LzdZEnbk15X6+1/+A+18f7xqZM0dkSqSwNviO14Sc/3snmZma0yswfMbN7IVpYyTtLDZvaimV3dy/aBfOeZ5DL1/Q9nNnyfkjTeObfLW94taXwvbbLte71KiZ7G3hzuZzwTfN4birupjyGNbPo+T5W0xzm3oY/tGfd99vg7EojfTwLOKGdmhZLulvQl51x9j80rlRjmOFbSTyXdN8LlpcopzrmFks6V9DkzO83vgtLFzGKSLpD0x142Z8v3+RYu0d+d1de7MLNvSuqUdGsfTTL9Z/wXkmZJOk7SLiWGb7LZ5eq/9yajvs/+/o74+ftJwHm7HZIqk15P8db12sbMIpJKJO0bkepSyMyiSvxQ3uqcu6fndudcvXOu0Vu+X1LUzMpHuMxhc87t8J5rJN2rRFd3soF855niXEkrnXN7em7Ilu/Ts6d7GNF7rumlTVZ8r2Z2paTzJX3I+2PxNgP4GQ8059we51yXcy4u6Qb1Xn+2fJ8RSRdJurOvNpn0ffbxdyQQv58EnLdbIWmOmc3w/m/4MknLe7RZLql7xvclkv7e1z88QeWNAf9a0jrn3P/00WZC99wiM1uixM9LRgU5Mysws6LuZSUmba7p0Wy5pI9awlJJdUndq5mmz/8zzIbvM0ny7+DHJP2plzYPSTrLzMZ4Qx5neesyhpmdI+lrki5wzjX30WYgP+OB1mPO2/vVe/0D+bc5E7xb0mvOuereNmbS99nP35Fg/H76PQs7iA8lzqp5XYkZ+9/01n1XiX9kJClXiSGAjZJekDTT75qHcIynKNFt+Iqkl73HeZI+LenTXpvPS1qrxNkKz0k6ye+6h3CcM736V3nH0v19Jh+nSbrO+75XS1rsd91DPNYCJQJLSdK6jP8+lQhsuyR1KDFO/wkl5rz9TdIGSY9KKvPaLpZ0Y9J7r/J+TzdK+rjfxzKE49yoxDyF7t/R7rM3J0m631vu9Wc8qI8+jvN33u/eK0r8cZzY8zi912/7tzmoj96O01t/c/fvZFLbjPw++/k7EojfT27VAAAAsg5DVAAAIOsQcAAAQNYh4AAAgKxDwAEAAFmHgAMAALIOAQcAAGQdAg4AAMg6BBwAAJB1CDgAACDrEHAAAEDWIeAAAICsE/G7gFQrLy9306dP97sMAAAwAl588cW9zrmKnuuzLuBMnz5dVVVVfpcBAABGgJlt7W09Q1QAACDrEHAAAEDWIeAAAICsQ8ABAABZh4ADAACyDgEHAABkHQIOAADIOgQcAACQdQg4AAAg6/gWcMys0sweM7NXzWytmX2xlzZmZj8xs41m9oqZLfSjVgAAkFn8vFVDp6QvO+dWmlmRpBfN7BHn3KtJbc6VNMd7nCjpF94zAABAn3zrwXHO7XLOrfSWGyStkzS5R7MLJf3WJTwnqdTMJo5wqZKkmoZWfetPa7S6us6PjwcAAIMQiDk4ZjZd0vGSnu+xabKk7Umvq/X2ECQzu9rMqsysqra2Ni01NrR26rfPbtWmvY1p2T8AAEgd3wOOmRVKulvSl5xz9UPZh3PueufcYufc4oqKt90xPSVi4cR/qo4ul5b9AwCA1PE14JhZVIlwc6tz7p5emuyQVJn0eoq3bsRFDwWcuB8fDwAABsHPs6hM0q8lrXPO/U8fzZZL+qh3NtVSSXXOuV0jVmSSSNgkEXAAAMgEfp5FdbKkj0habWYve+v+TdJUSXLO/VLS/ZLOk7RRUrOkj498mQlRhqgAAMgYvgUc59xTkuwwbZykz41MRf2L0oMDAEDG8H2ScaY41IPTScABACDoCDgDFAl5PThxhqgAAAg6As4AmZmiYWOICgCADEDAGYRoOKROAg4AAIFHwBmEaDjEWVQAAGQAAs4gRMOmdnpwAAAIPALOIDBEBQBAZiDgDEIkbAxRAQCQAQg4gxANhxiiAgAgAxBwBiHGEBUAABmBgDMIDFEBAJAZCDiDkDhNnB4cAACCjoAzCAQcAAAyAwFnEKIMUQEAkBEIOIPAdXAAAMgMBJxBiIRCaqcHBwCAwCPgDEIswt3EAQDIBAScQWCICgCAzEDAGYRIiLuJAwCQCQg4gxCLcDdxAAAyAQFnEBiiAgAgMxBwBoEhKgAAMgMBZxCinEUFAEBGIOAMQjTErRoAAMgEBJxBiIZDijupK84wFQAAQUbAGYRoxCSJXhwAAAKOgDMI0VDiPxcBBwCAYCPgDEI03N2DwxAVAABBRsAZhGgk8Z+La+EAABBsBJxB6B6i4mrGAAAEGwFnELonGXcyRAUAQKARcAYhwiRjAAAyAgFnEKJhhqgAAMgEBJxBiDFEBQBARiDgDAJDVAAAZAYCziAwRAUAQGYg4AwCQ1QAAGQGAs4gMEQFAEBmIOAMQvcQFbdqAAAg2Ag4g/DmvajowQEAIMgIOIPwZg8OAQcAgCAj4AzCmzfbZIgKAIAgI+AMQjSUGKLiNHEAAIKNgDMIDFEBAJAZCDiDwBAVAACZgYAzCBGGqAAAyAgEnEGIMUQFAEBGIOAMQihkCoeMgAMAQMD5GnDM7CYzqzGzNX1sP93M6szsZe/xrZGusadYOKT2TgIOAABBFvH582+W9DNJv+2nzZPOufNHppzDi0UIOAAABJ2vPTjOuSck7fezhsGKRUJMMgYAIOAyYQ7OMjNbZWYPmNm83hqY2dVmVmVmVbW1tWktJhYOqY0eHAAAAi3oAWelpGnOuWMl/VTSfb01cs5d75xb7JxbXFFRkdaCGKICACD4Ah1wnHP1zrlGb/l+SVEzK/ezplg4xFlUAAAEXKADjplNMDPzlpcoUe8+P2uiBwcAgODz9SwqM7td0umSys2sWtK3JUUlyTn3S0mXSPqMmXVKapF0mXPO1/skMMkYAIDg8zXgOOcuP8z2nylxGnlgcB0cAACCL9BDVEHEEBUAAMFHwBmkWITTxAEACDoCziAxBwcAgOAj4AwSc3AAAAg+As4gcR0cAACCj4AzSEwyBgAg+Ag4g0TAAQAg+Ag4g8QkYwAAgo+AM0iJOThO8bivF1QGAAD9IOAMUiyS+E9GLw4AAMFFwBmkWJiAAwBA0BFwBqm7B6eDicYAAAQWAWeQGKICACD4CDiDdGiIih4cAAACi4AzSId6cAg4AAAEFgFnkLoDDncUBwAguAg4g8QcHAAAgo+AM0jMwQEAIPgIOIN06DRxenAAAAgsAs4g0YMDAEDwEXAGibOoAAAIPgLOIDHJGACA4CPgDFL3EBWniQMAEFwEnEHKYYgKAIDAI+AMEnNwAAAIPgLOIEXDzMEBACDoCDiDdOg6OPTgAAAQWAScQYqETGb04AAAEGQEnEEyM8XCIebgAAAQYAScIYhFQpwmDgBAgBFwhiAnEmKICgCAACPgDAFDVAAABBsBZwiiEQIOAABBRsAZghwCDgAAgUbAGYLcaFhtnV1+lwEAAPpAwBmCnEhIrR304AAAEFQEnCHIidCDAwBAkBFwhiA3ynVwAAAIMgLOEOREwmrtoAcHAICgIuAMQQ5XMgYAINAIOEOQwxAVAACBRsAZAoaoAAAINgLOENCDAwBAsBFwhiAnElZ7Z1zOOb9LAQAAvSDgDEFuNPGfjV4cAACCiYAzBDmRsCSpjasZAwAQSAScIciJdPfgMNEYAIAgihyugZktlnSqpEmSWiStkfSIc+7AcD/czG6SdL6kGufc/F62m6QfSzpPUrOkK51zK4f7ucOVG/V6cBiiAgAgkPrswTGzj5vZSknfkJQnab2kGkmnSHrUzG4xs6nD/PybJZ3Tz/ZzJc3xHldL+sUwPy8luntwOFUcAIBg6q8HJ1/Syc65lt42mtlxSgSPbUP9cOfcE2Y2vZ8mF0r6rUucrvScmZWa2UTn3K6hfmYqvDlERQ8OAABB1GfAcc5d198bnXMvp7yat5ssaXvS62pvna8B580hKnpwAAAIosNOMjaza82s2MyiZvY3M6s1sw+PRHEDZWZXm1mVmVXV1tam/fPeHKKiBwcAgCAayFlUZznn6pWYDLxF0mxJX01nUUl2SKpMej3FW/cWzrnrnXOLnXOLKyoq0l5UDj04AAAE2kACTvcw1nsk/dE5V5fGenpaLumjlrBUUp3f82+kpAv90YMDAEAgHfY0cUl/MbPXlDhF/DNmViGpNRUfbma3SzpdUrmZVUv6tqSoJDnnfinpfiVOEd+oxGniH0/F5w5X94X+WunBAQAgkPoMOGY2yTm30zn3dTO7Voneky4za1bi7KZhc85dfpjtTtLnUvFZqXToLCp6cAAACKT+enBuNLMySY9LelDSU5LknGuS1JT+0oKLC/0BABBs/Z0mfp6Z5SoxhPR+ST80s21KhJ0HnXNDvv5NpuNCfwAABFu/c3Ccc63yAo0kmdkMJa4u/DMzm+CcW5L+EoOHC/0BABBsA5lkLEkys2JJdZLu8B6N6Soq6CLhkCIh4zRxAAACaiA32/wnSd9R4swp5612zrmZ6Sws6HIiIS70BwBAQA2kB+crkuY75/amu5hMkhMN04MDAEBADeRCf28ocQ0aJMmJhDhNHACAgBpID843JD1jZs9Laute6Zz7QtqqygC50bBamWQMAEAgDSTg/ErS3yWtlsRfdE+iB4chKgAAgmggASfqnPuXtFeSYXIiIU4TBwAgoAYyB+cBM7vazCaaWVn3I+2VBVxONMyF/gAACKiB9OB03y/qG0nrnKRRf5p4Q2un32UAAIBeHDbgOOdmjEQhmSYnElZtR9vhGwIAgBHX5xCVmZ3S3xvNrNjM5qe+pMyQFwszBwcAgIDqrwfnYjO7Von7UL0oqVZSrqTZkt4paZqkL6e9woDKj4bV0s4cHAAAgqi/u4n/f95k4oslXSppoqQWSesk/co599TIlBhMebGwWphkDABAIB3ubuL7Jd3gPZAkN0rAAQAgqAZymjh6kRcNq70zrq64O3xjAAAwogg4Q5QXS/ynoxcHAIDgIeAMUV40LElMNAYAIIAOG3DM7EUz+5yZjRmJgjJFXiwxfYmrGQMAEDwD6cH5oKRJklaY2R1mdraZWZrrCrxDPTgEHAAAAuewAcc5t9E5901JR0i6TdJNkraa2XdG8z2pDs3BYYgKAIDAGdAcHDNbIOm/Jf1A0t1KXBenXtLf01dasOXSgwMAQGAd9l5UZvaipIOSfi3p68657hswPW9mJ6extkBjiAoAgOAayN3EL3XObUpeYWYznHObnXMXpamuwMuLcRYVAABBNZAhqrsGuG5U4TRxAACCq88eHDM7UtI8SSVmltxTU6zETTdHtUM9OAxRAQAQOP0NUc2VdL6kUknvTVrfIOlTaawpI3T34HAdHAAAgqe/u4n/SdKfzGyZc+7ZEawpI+QyRAUAQGD1N0T1NefctZKuMLPLe253zn0hrZUFXDQcUjRsDFEBABBA/Q1RrfOeq0aikEyUGw0TcAAACKD+hqj+7D3fMnLlZJa8aJghKgAAAmggN9t8xMxKk16PMbOH0lpVhsiP0YMDAEAQDeQ6OBXOuYPdL5xzBySNS1tFGSSXHhwAAAJpIAGny8ymdr8ws2mSXPpKyhx59OAAABBIA7lVwzclPWVm/5Bkkk6VdHVaq8oQedEw18EBACCADhtwnHMPmtlCSUu9VV9yzu1Nb1mZIS8aVn1rh99lAACAHgbSgyNJJ0k6Len1X9JQS8bJjTEHBwCAIBrIWVTfk/RFSa96jy+a2f9Nd2GZID8aVmtH3O8yAABADwPpwTlP0nHOubgkmdktkl6S9G/pLCwT5MXCam7v9LsMAADQw0DOopISN9zsVpKGOjJSXjSsZoaoAAAInIH04Pw/SS+Z2WNKnEV1mqSvp7WqDJEXC6utM66uuFM4ZH6XAwAAPAM5i+p2M3tc0gneqn91zu1Oa1UZojAn8Z+vub1TRblRn6sBAADd+rub+MIeq6q950lmNsk5tzJ9ZWWG/Fh3wOki4AAAECD99eD8dz/bnKR3pbiWjFOQE5YkNbZ1arzPtQAAgDf1dzfxd45kIZmooLsHp42JxgAABMlAroOTb2b/bmbXe6/nmNn56S8t+PK9HpwmThUHACBQBnKa+G8ktStxNWNJ2iHpP1Px4WZ2jpmtN7ONZva2M7PM7EozqzWzl73HJ1PxuanS3YPT1EbAAQAgSAZymvgs59wHzexySXLONZvZsM+JNrOwpOsknanEBOYVZrbcOfdqj6Z3Ouc+P9zPS4cC7yyqJq6FAwBAoAykB6fdzPKUmFgsM5slqS0Fn71E0kbn3CbnXLukOyRdmIL9jpjuScbN9OAAABAoAwk410h6UFKlmd0q6W+SvpaCz54saXvS62pvXU8Xm9krZnaXmVX2tiMzu9rMqsysqra2NgWlDUz3aeKNBBwAAAKlz4BjZteZ2cnOuYclXSTpSkm3S1rsnHt8ZMrTnyVNd84tkPSIpFt6a+Scu945t9g5t7iiomKESpMKYl4PDkNUAAAESn89OK9L+qGZbZH0r5J2Ouf+4pzbm6LP3iEpuUdmirfuEOfcPudc93DYjZIWpeizUyISDiknEuIsKgAAAqbPgOOc+7Fzbpmkd0jaJ+kmM3vNzL5tZkek4LNXSJpjZjPMLCbpMknLkxuY2cSklxdIWpeCz02pgpwIZ1EBABAwh52D45zb6pz7vnPueEmXS3qfUhA0nHOdkj4v6SFvf39wzq01s++a2QVesy+Y2VozWyXpC0oMkwVKQU6YC/0BABAwhz1N3Mwiks5VooflDEmPKzHxeNicc/dLur/Hum8lLX9D0jdS8VnpUhCLMEQFAEDA9HezzTOV6LE5T9ILSpzGfbVzrmmEassI+bGwmujBAQAgUPrrwfmGpNskfdk5d2CE6sk4BTkRThMHACBg+rvZ5qi/W/hAFMQiqqlPxXUPAQBAqgzkQn/oR35OmB4cAAAChoAzTIU5ETUzyRgAgEAh4AxTfizCzTYBAAgYAs4wFcTCau+Mq6Mr7ncpAADAQ8AZpoKcxDxtLvYHAEBwEHCGqSAnccPNRubhAAAQGAScYSrMiUqSGlsJOAAABAUBZ5iKchNDVA2tHT5XAgAAuhFwhunNgEMPDgAAQUHAGaai3MQQVT09OAAABAYBZ5iKvR6cenpwAAAIDALOMHX34DAHBwCA4CDgDFNuNKRo2JiDAwBAgBBwhsnMVJQbpQcHAIAAIeCkQFFuhB4cAAAChICTAgQcAACChYCTAkU5DFEBABAkBJwUoAcHAIBgIeCkQGKSMQEHAICgIOCkQFFuRPUtDFEBABAUBJwUKM6NqLG9U/G487sUAAAgAk5KFOVG5ZzU2M4wFQAAQUDASYHiPO4oDgBAkBBwUoD7UQEAECwEnBQoyqUHBwCAICHgpEB3Dw5nUgEAEAwEnBQozUsEnIPNBBwAAIKAgJMCY/JjkqSD9OAAABAIBJwUKMqNKGTSweZ2v0sBAAAi4KREKGQqyYsyRAUAQEAQcFKkND/GEBUAAAFBwEmRRA8OQ1QAAAQBASdFxuQzRAUAQFAQcFKkND+mA/TgAAAQCAScFCnNj6qOHhwAAAKBgJMipXkxNbR1qqMr7ncpAACMegScFCnNT1zNuI4zqQAA8B0BJ0W6Aw4TjQEA8B8BJ0VKu2/XwERjAAB8R8BJkTH04AAAEBgEnBQpzUv04HCqOAAA/iPgpEhpAT04AAAEBQEnRYpyIoqFQ9rb1OZ3KQAAjHoEnBQxM40tjGlfI0NUAAD4jYCTQuWFOdrbSA8OAAB+8zXgmNk5ZrbezDaa2dd72Z5jZnd62583s+k+lDlg9OAAABAMvgUcMwtLuk7SuZKOlnS5mR3do9knJB1wzs2W9CNJ3x/ZKgeHHhwAAIIh4uNnL5G00Tm3SZLM7A5JF0p6NanNhZKu8ZbvkvQzMzPnnBvJQgeqvDBH+xrb5ZyTmfldDgBgFHDOKe6kuHOKOyd3aDnx7OJvbou7vtsfepbkvHbdy93bnbznt7RN7E/q3seb740n3qRjppSoKDc6ov9d/Aw4kyVtT3pdLenEvto45zrNrE7SWEl7kxuZ2dWSrpakqVOnpqvewyovjKm9K6761k6V5I3sFwkAmcQ5p44up854PPHcFVdX3Kkjnlju3tbZ5dTZc13cqavLqcs5xeOJ7XHn1BVPeiRt6zq0XeqKxxPPA3xv3Ht9aNlrn7zfzi73lkDxZohwisfVI3T0EkBcPwEkfvj2meBPnztZx1aWjuhn+hlwUsY5d72k6yVp8eLFvn3d5YU5kqS9jW0EHAAjznl/eNs742rvjKujK662zrjau9583b2te13Pbd3tOzqd2ru6ktq7pPZd6uhy6uhKBJBEMEksd3TFDwWSxPNbQ0xHUpDwWzhkCpspFJIioZBC5q3rfpgpFDJFQonnsNlbtoeSXkdCIYVDJjMpZKaQ92xJy6GQvNfJ2/tpbz3aH27/Pdv33H+o7/YmJepT4j3mret+f/fym+u739/LukP7eHN51rjCEf9+/Qw4OyRVJr2e4q3rrU21mUUklUjaNzLlDd7YwsTVjPc1tmtWhc/FAAiEeNyptbNLTW1damnvUlN7p1o6utTa0aW2jrhaO7rU2tml1u7lpHWHtnev7+x6S5u2zrdub+vsSun/0YdDplg4pFgkpGg4pJxIYjkWDikaSfxRj4YTf+ALoxFFQqZIOLEuEgopErY313nPkbAp6oWBaNhbFzJFw0ntvfdGk7aFQ3ZoXbg7dFhiXXcQ6S2AHAonSe9JbBNTCbKcnwFnhaQ5ZjZDiSBzmaQrerRZLuljkp6VdImkvwd1/o301h4cAJknHndqau9UQ2unGtsSzw2tHWpu71Jze5da2jvV5C03t3WqucN77l7X3vvyUMQiIeVGQsqNhr2HtxwJqyg3ooqiHOUc2h5SbiTR7lAI8UJJLJIIJtFw6FBY6T2wvLm9u304RABA5vIt4Hhzaj4v6SFJYUk3OefWmtl3JVU555ZL+rWk35nZRkn7lQhBgdUdcPYRcIARF487NbR26mBLu+paOlTX0qHGVi+ktCWCSmNycGnrVGNrx1vCTGNb54A/Lz8W9h6RQ8sFORGVF+aoICeivFhYBbGw8mIRFfRomxsLe4GkR4BJCikhwgUwLL7OwXHO3S/p/h7rvpW03Crp0pGua6jG5EdlJtVyLRxgyNo74zrQ3K4Dze2qa+7QwZYO1TUnAkt3eDnovU5erm/t0OH6d/NjYRXmRFSUG1FhblRFORGNL85VYU5EhbkRFXnrEsuRQ23zYxEVxLzQkpMIJwQQINiyYpJxUETCIZXlx1TbQA8O0K21o0v7mtq1v7Fd+5ratL+pXfub2pPWtWu/t35fU7saWvvuRQmHTCV5UZXmRVWcF1VZQUwzygtUmhdVSV5UJfmxpOXomyElJ6qCnLAiYS7eDowWBJwUG1ecq5r6Vr/LANIqHnfa19SumoZW1Ta0qaahLfFc36qapNd7G9v6nIMSCZnKCmIqK4hpbGFMx4wp1VjvdVlBTGPyYyrN98JKXlSl+VEV5kSYGApgQAg4KTaxJFe7CTjIYE1tndpV16KdB1sPPdc0tKqmvs0LL63a29je62m+xbkRjSvO1biiHB0/tVTlhTmJAJMUZMoKEuuKcwkrANKHgJNiE0pytWr7Qb/LAHrV1tml3XWtSeGlRTvrWrXrYIt21bVq58EW1fcYIjKTxhbkaFxRjsYV5+ioiUUaV5SrccWJdRVFORpXlKuKohzlRsM+HRkAvBUBJ8UmFudqX1O7Wju6+MceIy4ed6ptbNP2/c3atr9Z2/e3JJ4PNGv7/mbtrm9920TcsoKYJpbkasqYfC2ZUaaJJXmaVJqriSV5mliSq/HFuYpFmLsCILMQcFJsfEmuJKmmvk1Tx+b7XA2yUWdXXNUHWrR5b5PeqG30gkwi0FQfaFFbZ/xQWzNpfFGuppbla9mssZpalq/JpXmaVJoILxNL8pQXI4gDyD4EnBSb6AWc3fWtBBwMmXNOexvbtam2UZv3NmnT3iZtqm3S5r2JQNPR9WY3TFFuRFPL8jVnXJHOOGq8KsfkqbIsX5VemKEnEcBoRMBJse6As6uuxedKkAmcc9pd36r1uxu0YU+j1u9p0IY9DdpU26SGpIvOxcIhTS/P1+xxhTpr3gTNKC/QrIoCzSgvVFlBzMcjAIBgIuCk2ISSPEnS7jrOpMJb7W1s0+u7G/T6ngat39Oo1/cklpOv+1JemKMjxhfqfcdP1syKAi/IFGpSaR6XzQeAQSDgpFhhTuLCYrsIOKNWPO60dX+z1u6s09qd9Vq7s16v7qzT3qQrXJfmR3XE+CJdeNwkzR1fpDnji3TE+CJ6YwAgRQg4aTChJFd7uBbOqNDRFdfrexq8EFOvtTvrtG5Xw6F7GkXDpjnjivTOueN05MRizR1fpCMmFKqiMIdrwABAGhFw0mBiSa52HGQOTrZxzqn6QIte2n5QL287qJe3H9CanfVq985ayo+FddTEYl20cLLmTSrWvEklmjO+UDkRJvkCwEgj4KRBZVm+1qze5XcZGKb61g6tOhRmDmpV9cFDw0w5kZDmTy7RR5ZO04IpJZo3qUQzyguYJwMAAUHASYNpZfk60Jy4u3FxbtTvcjBAu+ta9cKW/Vqxeb9WbNmv9XsaDl0Ub1ZFgd5xxDgdN7VUx1eWau6EIkW5cSMABBYBJw2mliWuf7N9f7PmTSrxuRr0xjmnzXubtGLLfr2w+YBWbNmvbfubJSWGmhZNG6Nz50/UwmmlWjClVCV5BFUAyCQEnDSoJOAEUvWBZj29ca+e3rhPz7yxT3sb2yQlblWweNoYfXTZNJ0wvUzzJhUrQu8MAGQ0Ak4adF/BeOu+Zp8rGd0ONrfr2Tf26amNe/X0xr3a4n0f5YU5Onn2WJ04Y6yWzBijWRWFnNEEAFmGgJMGxblRleZHDw15YGR0dsX10vaDeuy1Gj25Ya/W7KyTc1JBLKylM8fqo8um65Q55ZozjkADANmOgJMmU8vyCTgjYF9jm/7xeq0eW1+rJ16vVV1LhyIh0/FTS/WlM47QKXPGasGUUiYEA8AoQ8BJk6ll+Vq9o87vMrKOc05rd9br76/V6O+v1WhV9UE5lxh2OvPo8XrXkeN0ypxyzl4DgFGOgJMmM8oL9MCa3Wrr7OJCb8PUFXeq2rJfD67drYfX7tGOgy0ykxZMSfTSvPPICs2fVKIQ16ABAHgIOGkye1yhuuJOW/Y2a+6EIr/LyTjtnXE988ZePeSFmn1N7YpFQjptTrm++O45eteR41RemON3mQCAgCLgpMmccYlQ8/qeBgLOAHV0xfXkhlr9edUuPbpujxpaO1UQC+tdR43XOfMm6B1zK1SYw48sAODw+GuRJjMrChQyaUNNo9+lBFo87rRiy34tX7VT96/epQPNHSrJi+rc+RN0zvwJOmlWuXKjDPEBAAaHgJMmudGwppbla2NNg9+lBE73ROE/r9qp5at2alddq/KiYZ159HhdeNwknTqnQrEIZz0BAIaOgJNGc8YXacMeenC61Ta06b6XdugPVdu1oaZRkZDpHUdU6OvnHqkzjx6v/Bg/jgCA1OAvShrNGVeox16rUXtnfNT2SHR0xfX4+lr9oWq7HnutRp1xp4VTS/Vf75+v8+ZP1JiCmN8lAgCyEAEnjeZOKFJn3GlDTcOouyfVxpoG/bGqWnev3KG9jW0qL8zRJ06ZoUsXT9HscUy6BgCkFwEnjY6dUipJeqW6blQEnI6uuB5au1u/e3arnt+8X5GQ6V1HjtMHFlfqHXMruJowAGDEEHDSaNrYfBXnRvRKdZ0uX+J3Nemzu65Vt72wTbe/sE21DW2aMiZP/3rOkbpk0RRVFHGtGgDAyCPgpJGZacGUUr1SfdDvUlLOOadn39in3z23VQ+/ukdx53T6ERX6yLJpescR4xTmqsIAAB8RcNLsmCkluuGJTWrt6MqK67m0d8a1fNVO3fjkJr22u0Gl+VF98pQZ+tCJ0zR1bL7f5QEAIImAk3bHTilRZzxx3ZdF08b4Xc6QHWxu163Pb9Mtz2xRTUOb5o4v0rWXLNAFx07KiuAGAMguBJw0WzStTJL0/OZ9GRlwtu5r0k1PbdYfqqrV0tGlU+eU6weXHqvT5pTLjGEoAEAwEXDSrKIoR0eML9Szb+zTZ0+f7Xc5A7Z+d4Oue2yj/vLKToVDpguOnaxPnjpDR00s9rs0AAAOi4AzAk6aVa47VmzLiAv+ra6u088e26CH1u5RQSysT506U1edMkPji3P9Lg0AgAEj4IyAZbPG6uZntujl7Qe1ZEaZ3+X06sWtB/Szv2/QY+trVZQb0RfOmKOPnzSdKw0DADISAWcELJ0xVpGQ6bH1NYELOCu27NePHnldz7yxT2UFMX317Ln6yLJpKs6N+l0aAABDRsAZASX5US2bNVYPrtmtr509NxCTc9fsqNMPH16vx9fXqqIoR//+nqN0xYlTueElACAr8NdshJwzf4K+ee8ard/ToCMn+DdRd2NNo370yOv66+pdKs2P6hvnHqmPLpuuvBinegMAsgcBZ4ScdfQE/ft9a/TXV3b5EnCqDzTrx49u0N0rq5UXDesLZ8zRJ0+dwVAUACArEXBGSEVRjk6bU6E/VG3XF86YM2I3nqxpaNV1f9+o217YJjPTVSfP0GdOn6WxhdwjCgCQvQg4I+jDS6fpU7+t0qOv7tG5x0xM62fVNXfol0+8oZuf3qL2rrg+sLhSXzhjtiaW5KX1cwEACAICzgh615HjNLk0Tzc+tVnnzJ+QlsnGTW2d+s3Tm/WrJzapsa1TFxw7Sf/fu4/Q9PKClH8WAABBRcAZQeGQ6dOnz9J/3LdGj62v0buOHJ+yfbd2dOm257fpusc2al9Tu9591Dh9+ay5XHkYADAqEXBG2GUnVOrGJzfp/93/mk6aVT7sG1V2dsV198pq/fjRDdpZ16qTZ4/Vl8+aq4VTM+++VwAApEqw7xuQhaLhkK65YJ421DTqhw+tH/J+Orri+mPVdp35oyf0r3ev1rjiXN36yRN16yeXEm4AAKMePTg+eOfccfrw0qm68anNmjO+UB88YeqA39vS3qU7V2zT9U9s0s66Vh01sVg3fHSx3n3UuEBcQBAAgCDwJeCYWZmkOyVNl7RF0geccwd6adclabX3cptz7oKRqjHd/uP8o7Vtf4u+fs9q1dS36bPvnK1wqO+A8truet3xwnbds7Ja9a2dOmH6GP3X+4/R6XMrCDYAAPRgzrmR/1CzayXtd859z8y+LmmMc+5fe2nX6JwrHMy+Fy9e7KqqqlJValq1tHfpG/e8ovte3qmZ5QW6fMlULZxWqrKCHDW3d2rz3ia9tO2gHnutRpv2NikWDuns+RP0kaXTAndPKwAA/GBmLzrnFr9tvU8BZ72k051zu8xsoqTHnXNze2mX1QFHkpxzemjtHl332Eat3lH3tu2xSEhLZ47VGUeO03uPnaQy7u4NAMAhQQs4B51zpd6ySTrQ/bpHu05JL0vqlPQ959x9fezvaklXS9LUqVMXbd26NS11p9uOgy3asKdBB5rblRcNa2pZgWZWFAz7TCsAALJVXwEnbXNwzOxRSRN62fTN5BfOOWdmfaWsac65HWY2U9LfzWy1c+6Nno2cc9dLul5K9OAMs3TfTC7N0+RSrjQMAMBwpS3gOOfe3dc2M9tjZhOThqhq+tjHDu95k5k9Lul4SW8LOAAAAMn8ug7Ockkf85Y/JulPPRuY2Rgzy/GWyyWdLOnVEasQAABkLL8CzvcknWlmGyS923stM1tsZjd6bY6SVGVmqyQ9psQcHAIOAAA4LF+ug+Oc2yfpjF7WV0n6pLf8jKRjRrg0AACQBbhVAwAAyDoEHAAAkHUIOAAAIOsQcAAAQNYh4AAAgKxDwAEAAFmHgAMAALIOAQcAAGQdX+4mnk5mVispnbcTL5e0N437D4LRcIwSx5ltOM7swnFml3Qe5zTnXEXPlVkXcNLNzKp6uy17NhkNxyhxnNmG48wuHGd28eM4GaICAABZh4ADAACyDgFn8K73u4ARMBqOUeI4sw3HmV04zuwy4sfJHBwAAJB16MEBAABZh4ADAACyDgGnF2Z2jpmtN7ONZvb1XrbnmNmd3vbnzWy6D2UOi5lVmtljZvaqma01sy/20uZ0M6szs5e9x7f8qHW4zGyLma32jqGql+1mZj/xvs9XzGyhH3UOh5nNTfqeXjazejP7Uo82Gfl9mtlNZlZjZmuS1pWZ2SNmtsF7HtPHez/mtdlgZh8buaoHr4/j/IGZveb9XN5rZqV9vLffn/Eg6eM4rzGzHUk/m+f18d5+/20Okj6O886kY9xiZi/38d6M+D77+jsSmN9P5xyPpIeksKQ3JM2UFJO0StLRPdp8VtIvveXLJN3pd91DOM6JkhZ6y0WSXu/lOE+X9Be/a03BsW6RVN7P9vMkPSDJJC2V9LzfNQ/zeMOSditx8auM/z4lnSZpoaQ1SeuulfR1b/nrkr7fy/vKJG3ynsd4y2P8Pp5BHudZkiLe8vd7O05vW78/40F69HGc10j6ymHed9h/m4P06O04e2z/b0nfyuTvs6+/I0H5/aQH5+2WSNronNvknGuXdIekC3u0uVDSLd7yXZLOMDMbwRqHzTm3yzm30ltukLRO0mR/q/LNhZJ+6xKek1RqZhP9LmoYzpD0hnMunVf0HjHOuSck7e+xOvl38BZJ7+vlrWdLesQ5t985d0DSI5LOSVedw9XbcTrnHnbOdXovn5M0ZcQLS7E+vs+BGMi/zYHR33F6fy8+IOn2ES0qxfr5OxKI308CzttNlrQ96XW13v6H/1Ab7x+fOkljR6S6NPCG2I6X9Hwvm5eZ2Soze8DM5o1sZSnjJD1sZi+a2dW9bB/Id55JLlPf/3Bmw/cpSeOdc7u85d2SxvfSJtu+16uU6GnszeF+xjPB572huJv6GNLIpu/zVEl7nHMb+tiecd9nj78jgfj9JOCMcmZWKOluSV9yztX32LxSiWGOYyX9VNJ9I1xeqpzinFso6VxJnzOz0/wuKF3MLCbpAkl/7GVztnyfb+ES/d1Zfb0LM/umpE5Jt/bRJNN/xn8haZak4yTtUmL4Jptdrv57bzLq++zv74ifv58EnLfbIaky6fUUb12vbcwsIqlE0r4RqS6FzCyqxA/lrc65e3pud87VO+caveX7JUXNrHyEyxw259wO77lG0r1KdHUnG8h3ninOlbTSOben54Zs+T49e7qHEb3nml7aZMX3amZXSjpf0oe8PxZvM4Cf8UBzzu1xznU55+KSblDv9WfL9xmRdJGkO/tqk0nfZx9/RwLx+0nAebsVkuaY2Qzv/4Yvk7S8R5vlkrpnfF8i6e99/cMTVN4Y8K8lrXPO/U8fbSZ0zy0ysyVK/LxkVJAzswIzK+peVmLS5poezZZL+qglLJVUl9S9mmn6/D/DbPg+kyT/Dn5M0p96afOQpLPMbIw35HGWty5jmNk5kr4m6QLnXHMfbQbyMx5oPea8vV+91z+Qf5szwbslveacq+5tYyZ9n/38HQnG76ffs7CD+FDirJrXlZix/01v3XeV+EdGknKVGALYKOkFSTP9rnkIx3iKEt2Gr0h62XucJ+nTkj7ttfm8pLVKnK3wnKST/K57CMc506t/lXcs3d9n8nGapOu873u1pMV+1z3EYy1QIrCUJK3L+O9TicC2S1KHEuP0n1BiztvfJG2Q9KikMq/tYkk3Jr33Ku/3dKOkj/t9LEM4zo1KzFPo/h3tPntzkqT7veVef8aD+ujjOH/n/e69osQfx4k9j9N7/bZ/m4P66O04vfU3d/9OJrXNyO+zn78jgfj95FYNAAAg6zBEBQAAsg4BBwAAZB0CDgAAyDoEHAAAkHUIOAAAIOsQcAD4wszGJt1ZeXfS3aQbzeznafrML5nZR/vZfr6ZfTcdnw1gZHGaOADfmdk1khqdcz9M42dElLhdxUL35g0se7Yxr83Jro8L6wHIDPTgAAgUMzvdzP7iLV9jZreY2ZNmttXMLjKza81stZk96F0mXma2yMz+4d2c8KE+7gb/LiVuY9HpvecLZvaqd4PHO6RD9815XIlbIwDIYAQcAEE3S4lwcoGk30t6zDl3jKQWSe/xQs5PJV3inFsk6SZJ/9XLfk6W9GLS669LOt45t0CJKz53q1Libs8AMljE7wIA4DAecM51mNlqSWFJD3rrV0uaLmmupPmSHvFutRVW4hL5PU2UtC7p9SuSbjWz+/TWO6vXKHHpfAAZjIADIOjaJMk5FzezDvfmxMG4Ev+GmaS1zrllh9lPixL3kev2HkmnSXqvpG+a2THe8FWu1xZABmOICkCmWy+pwsyWSZKZRc1sXi/t1kma7bUJSap0zj0m6V8llUgq9NodoYDevRnAwBFwAGQ051y7pEskfd/MVilxR+OTemn6gBI9NlJiGOv33rDXS5J+4pw76G17p6S/prNmAOnHaeIARg0zu1fS15xzG/rYPl7Sbc65M0a2MgCpRsABMGqY2VxJ451zT/Sx/QRJHc65l0e0MAApR8ABAABZhzk4AAAg6xBwAABA1iHgAACArEPAAQAAWYeAAwAAss7/D6YL2YIz7L7GAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "DeltaT = 0.01\n", "#set up arrays \n", "tfinal = 20 # in seconds\n", "n = ceil(tfinal/DeltaT)\n", "# set up arrays for t, a, v, and x\n", "t = np.zeros(n)\n", "v = np.zeros(n)\n", "x = np.zeros(n)\n", "# Initial conditions as compact 2-dimensional arrays\n", "x0 = 2\n", "v0 = 2\n", "x[0] = x0\n", "v[0] = v0\n", "gamma = 2\n", "# Start integrating using Euler's method\n", "for i in range(n-1):\n", " # Set up the acceleration\n", " a = -2*gamma*v[i]-x[i]\n", " # update velocity, time and position using Euler's forward method\n", " v[i+1] = v[i] + DeltaT*a\n", " x[i+1] = x[i] + DeltaT*v[i+1]\n", " t[i+1] = t[i] + DeltaT\n", "m = 1\n", "k = 1\n", "# Plot position and velocity as function of time \n", "fig, ax = plt.subplots(2,1)\n", "fig.set_size_inches(8,10)\n", "ax[0].set_title('Overdamping')\n", "ax[0].plot(t,x)\n", "ax[1].plot(t,v)\n", "ax[1].set_xlabel('Time (s)')\n", "ax[0].set_ylabel('Position (m)')\n", "ax[1].set_ylabel('Velocity (m/s)')\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Underdamping occurs when the damping force is relatively weak, and the system oscillates with decreasing amplitude but still exhibits oscillatory behavior. The system takes longer to come to rest than it would in the absence of damping. In this case, 𝛾 is less than the critical damping value, which is the minimum amount of damping required to bring the system to rest as quickly as possible.\n", "\n", "Critical damping occurs when the damping force is just strong enough to bring the system to rest in the shortest possible time without oscillating. In this case, 𝛾 is equal to the critical damping value, and the system returns to its equilibrium position as quickly as possible without oscillating.\n", "\n", "Overdamping occurs when the damping force is very strong, and the system takes an extended time to return to its equilibrium position without oscillating. In this case, 𝛾 is greater than the critical damping value, and the system's motion is dominated by the damping force rather than the restoring force.\n", "\n", "The behavior of a damped oscillator depends on the relative strengths of the damping force and the restoring force. Understanding the different types of damping is essential in designing and analyzing mechanical and electrical systems that exhibit oscillatory behavior in the presence of damping. Numerical solutions of damped oscillations can be used to model and analyze these systems and predict their behavior under various conditions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Driven Oscillations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assume that our external driving force is given by" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "F_{\\mathrm{ext}}(t) = F_0\\cos{(\\omega t)},\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Introducing the external force into the differential equation and dividing by $m$ and introducing $\\omega_0^2=\\sqrt{k/m}$ we have" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{dt^2} + \\frac{b}{m}\\frac{dx}{dt}+\\omega_0^2x(t) =\\frac{F_0}{m}\\cos{(\\omega t)},\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thereafter we introduce a dimensionless time $\\tau = t\\omega_0$\n", "and a dimensionless frequency $\\tilde{\\omega}=\\omega/\\omega_0$. We have then" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{d\\tau^2} + \\frac{b}{m\\omega_0}\\frac{dx}{d\\tau}+x(\\tau) =\\frac{F_0}{m\\omega_0^2}\\cos{(\\tilde{\\omega}\\tau)},\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Introducing a new amplitude $\\tilde{F} =F_0/(m\\omega_0^2)$ (check dimensionality again) we have" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{d\\tau^2} + \\frac{b}{m\\omega_0}\\frac{dx}{d\\tau}+x(\\tau) =\\tilde{F}\\cos{(\\tilde{\\omega}\\tau)}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our final step, as we did in the case of various types of damping, is\n", "to define $\\gamma = b/(2m\\omega_0)$ and rewrite our equations as" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\frac{d^2x}{d\\tau^2} + 2\\gamma\\frac{dx}{d\\tau}+x(\\tau) =\\tilde{F}\\cos{(\\tilde{\\omega}\\tau)}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This gives us:\n", "\n", "$$\\frac{d^2x}{d\\tau^2} = - 2\\gamma v(t)-x(\\tau)+\\tilde{F}\\cos{(\\tilde{\\omega}\\tau)} \\text{ where } v(t) = \\frac{dx}{d\\tau}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical Solutions of Driven Oscillations\n", "\n", "### Euler-Cromer" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "DeltaT = 0.001\n", "#set up arrays \n", "tfinal = 20 # in dimensionless time\n", "n = ceil(tfinal/DeltaT)\n", "# set up arrays for t, v, and x\n", "t = np.zeros(n)\n", "v = np.zeros(n)\n", "x = np.zeros(n)\n", "# Initial conditions as one-dimensional arrays of time\n", "x0 = 2\n", "v0 = 2\n", "x[0] = x0\n", "v[0] = v0\n", "gamma = 0.2\n", "Omegatilde = 0.5\n", "Ftilde = 1.0\n", "# Start integrating using Euler-Cromer's method\n", "for i in range(n-1):\n", " # Set up the acceleration\n", " a = -2*gamma*v[i]-x[i]+Ftilde*cos(t[i]*Omegatilde)\n", " # update velocity, time and position\n", " v[i+1] = v[i] + DeltaT*a\n", " x[i+1] = x[i] + DeltaT*v[i+1]\n", " t[i+1] = t[i] + DeltaT\n", "# Plot position and velocity as function of time \n", "fig, ax = plt.subplots(2,1)\n", "fig.set_size_inches(8,10)\n", "ax[0].set_title('Driving Force')\n", "ax[0].plot(t,x)\n", "ax[1].plot(t,v)\n", "ax[1].set_xlabel('Time (s)')\n", "ax[0].set_ylabel('Position (m)')\n", "ax[1].set_ylabel('Velocity (m/s)')\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Runge-Kutta (Fourth Order)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "def SpringForce(v,x,t):\n", "# note here that we have divided by mass and we return the acceleration\n", " return -2*gamma*v-x+Ftilde*cos(t*Omegatilde)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "def RK4(v,x,t,n,Force):\n", " for i in range(n-1):\n", "# Setting up k1\n", " k1x = DeltaT*v[i]\n", " k1v = DeltaT*Force(v[i],x[i],t[i])\n", "# Setting up k2\n", " vv = v[i]+k1v*0.5\n", " xx = x[i]+k1x*0.5\n", " k2x = DeltaT*vv\n", " k2v = DeltaT*Force(vv,xx,t[i]+DeltaT*0.5)\n", "# Setting up k3\n", " vv = v[i]+k2v*0.5\n", " xx = x[i]+k2x*0.5\n", " k3x = DeltaT*vv\n", " k3v = DeltaT*Force(vv,xx,t[i]+DeltaT*0.5)\n", "# Setting up k4\n", " vv = v[i]+k3v\n", " xx = x[i]+k3x\n", " k4x = DeltaT*vv\n", " k4v = DeltaT*Force(vv,xx,t[i]+DeltaT)\n", "# Final result\n", " x[i+1] = x[i]+(k1x+2*k2x+2*k3x+k4x)/6.\n", " v[i+1] = v[i]+(k1v+2*k2v+2*k3v+k4v)/6.\n", " t[i+1] = t[i] + DeltaT" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "DeltaT = 0.001\n", "#set up arrays \n", "tfinal = 20 # in dimensionless time\n", "n = ceil(tfinal/DeltaT)\n", "# set up arrays for t, v, and x\n", "t = np.zeros(n)\n", "v = np.zeros(n)\n", "x = np.zeros(n)\n", "# Initial conditions (can change to more than one dim)\n", "x0 = 2 \n", "v0 = 2\n", "x[0] = x0\n", "v[0] = v0\n", "gamma = 0.2\n", "Omegatilde = 0.5\n", "Ftilde = 1.0\n", "# Start integrating using the RK4 method\n", "# Note that we define the force function as a SpringForce\n", "RK4(v,x,t,n,SpringForce)\n", "\n", "# Plot position and velocity as function of time \n", "fig, ax = plt.subplots(2,1)\n", "fig.set_size_inches(8,10)\n", "ax[0].set_title('Driving Force')\n", "ax[0].plot(t,x)\n", "ax[1].plot(t,v)\n", "ax[1].set_xlabel('Time (s)')\n", "ax[0].set_ylabel('Position (m)')\n", "ax[1].set_ylabel('Velocity (m/s)')\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Numerical solutions of driven oscillations involve using computational methods to solve differential equations that describe the behavior of systems that are subject to an external driving force. The differential equations can be solved numerically using various methods, including the Euler-Cromer and the Runge-Kutta fourth-order methods.\n", "\n", "The Euler-Cromer method is a straightforward and easy-to-implement numerical integration method that is commonly used to solve differential equations in physics and engineering. However, it can introduce errors that accumulate over time, leading to a loss of accuracy in the simulation. This method is also not very efficient for complex systems or systems with rapidly varying driving forces.\n", "\n", "In contrast, the Runge-Kutta fourth-order method is a more accurate and reliable numerical integration method that is widely used in simulations of driven oscillations. This method uses a set of equations to calculate the values of the system variables at each time step, resulting in more accurate predictions of the system's behavior. Additionally, the Runge-Kutta fourth-order method is more efficient for systems with rapidly varying driving forces, allowing for faster and more accurate simulations.\n", "\n", "Overall, the Runge-Kutta fourth-order method is considered to be a better choice than the Euler-Cromer method when simulating driven oscillations due to its higher accuracy, reliability, and efficiency. This method can provide more accurate predictions of the system's behavior under different driving conditions, helping engineers and physicists design and optimize systems that exhibit driven oscillations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Neural Networks" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Neural networks have become increasingly popular in recent years for modeling and predicting the behavior of physical systems, including damped and driven oscillations. These systems can exhibit complex and nonlinear behavior that can be challenging to understand and predict using traditional mathematical models.\n", "\n", "The code provided above demonstrates the use of a neural network to study a damped oscillation system with an external driving force. The system is modeled using a differential equation that describes the motion of a spring-mass system subject to an external driving force. The differential equation is solved using the scipy.integrate.solve_ivp function to generate training and validation data for the neural network.\n", "\n", "The neural network is implemented using the TensorFlow library in Python. The architecture consists of a Long Short-Term Memory (LSTM) layer followed by two fully connected layers with dropout regularization to prevent overfitting. The network is trained using the mean squared error loss function and the Adam optimizer.\n", "\n", "The code includes early stopping as a regularization technique to prevent overfitting of the model to the training data. The validation loss is monitored during training, and if it fails to improve for a specified number of epochs, the training is stopped and the weights of the best-performing model are restored.\n", "\n", "Overall, the use of neural networks for studying damped and driven oscillations allows for the prediction of complex and nonlinear behavior, which can be difficult to achieve with traditional mathematical models. The code provided serves as an example of how neural networks can be used to model and predict the behavior of physical systems, providing insights into their behavior under different conditions." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import tensorflow as tf\n", "from tensorflow.keras.layers import Dense, LSTM, Dropout\n", "from tensorflow.keras.models import Sequential\n", "from tensorflow.keras.optimizers import Adam\n", "from tensorflow.keras.regularizers import l2\n", "from tensorflow.keras.callbacks import EarlyStopping\n", "from scipy.integrate import solve_ivp\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "learning_rate = 0.001\n", "epochs = 1000\n", "hidden_layer_size = 64\n", "l2_regularization = 1e-4\n", "dropout_rate = 0.2" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "model = Sequential([\n", " LSTM(hidden_layer_size, activation='tanh', input_shape=(1, 3), kernel_regularizer=l2(l2_regularization)),\n", " Dropout(dropout_rate),\n", " Dense(hidden_layer_size, activation='relu', kernel_regularizer=l2(l2_regularization)),\n", " Dropout(dropout_rate),\n", " Dense(2)\n", "])\n", "\n", "optimizer = Adam(learning_rate=learning_rate)\n", "model.compile(optimizer=optimizer, loss='mse')" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "def SpringForce(t, y, gamma, Ftilde, Omegatilde):\n", " x, v = y\n", " a = -2*gamma*v-x+Ftilde*cos(t*Omegatilde)\n", " return [v, a]" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "gamma = 0.2\n", "Ftilde = 1.0\n", "Omegatilde = 0.5\n", "\n", "t_span = (0, 20)\n", "t_eval = np.linspace(*t_span, num=1000)\n", "initial_conditions = [2, 2]\n", "\n", "solution = solve_ivp(SpringForce, t_span, initial_conditions, args=(gamma, Ftilde, Omegatilde), t_eval=t_eval, method='RK45')\n", "t_train = solution.t\n", "y_train = solution.y.T" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "validation_split = 0.2\n", "split_index = int((1 - validation_split) * len(t_train))\n", "\n", "t_train, t_val = t_train[:split_index], t_train[split_index:]\n", "y_train, y_val = y_train[:split_index], y_train[split_index:]" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "input_train = np.column_stack((t_train, y_train))\n", "input_train = input_train[:, np.newaxis, :]\n", "\n", "input_val = np.column_stack((t_val, y_val))\n", "input_val = input_val[:, np.newaxis, :]" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch 1/1000\n", "25/25 [==============================] - 5s 27ms/step - loss: 0.9932 - val_loss: 0.9847\n", "Epoch 2/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.6206 - val_loss: 1.1054\n", "Epoch 3/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.2845 - val_loss: 0.6862\n", "Epoch 4/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.1508 - val_loss: 0.5876\n", "Epoch 5/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0904 - val_loss: 0.3317\n", "Epoch 6/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0776 - val_loss: 0.2523\n", "Epoch 7/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0681 - val_loss: 0.2011\n", "Epoch 8/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0594 - val_loss: 0.1479\n", "Epoch 9/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0564 - val_loss: 0.1409\n", "Epoch 10/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0546 - val_loss: 0.1538\n", "Epoch 11/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0551 - val_loss: 0.1175\n", "Epoch 12/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0510 - val_loss: 0.1400\n", "Epoch 13/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0509 - val_loss: 0.1371\n", "Epoch 14/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0468 - val_loss: 0.1022\n", "Epoch 15/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0436 - val_loss: 0.1038\n", "Epoch 16/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0486 - val_loss: 0.0790\n", "Epoch 17/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0416 - val_loss: 0.0797\n", "Epoch 18/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0400 - val_loss: 0.0812\n", "Epoch 19/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0432 - val_loss: 0.0821\n", "Epoch 20/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0425 - val_loss: 0.0939\n", "Epoch 21/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0411 - val_loss: 0.0838\n", "Epoch 22/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0429 - val_loss: 0.0788\n", "Epoch 23/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0409 - val_loss: 0.0886\n", "Epoch 24/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0407 - val_loss: 0.0917\n", "Epoch 25/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0407 - val_loss: 0.0651\n", "Epoch 26/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0384 - val_loss: 0.0877\n", "Epoch 27/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0372 - val_loss: 0.0887\n", "Epoch 28/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0395 - val_loss: 0.0677\n", "Epoch 29/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0368 - val_loss: 0.0617\n", "Epoch 30/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0367 - val_loss: 0.0834\n", "Epoch 31/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0368 - val_loss: 0.0486\n", "Epoch 32/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0382 - val_loss: 0.0872\n", "Epoch 33/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0366 - val_loss: 0.0880\n", "Epoch 34/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0363 - val_loss: 0.0681\n", "Epoch 35/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0359 - val_loss: 0.0598\n", "Epoch 36/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0375 - val_loss: 0.0610\n", "Epoch 37/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0354 - val_loss: 0.0645\n", "Epoch 38/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0358 - val_loss: 0.0996\n", "Epoch 39/1000\n", "25/25 [==============================] - 0s 7ms/step - loss: 0.0389 - val_loss: 0.0878\n", "Epoch 40/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0340 - val_loss: 0.0891\n", "Epoch 41/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0320 - val_loss: 0.0818\n", "Epoch 42/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0347 - val_loss: 0.0789\n", "Epoch 43/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0326 - val_loss: 0.0638\n", "Epoch 44/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0342 - val_loss: 0.0837\n", "Epoch 45/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0333 - val_loss: 0.0889\n", "Epoch 46/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0316 - val_loss: 0.0910\n", "Epoch 47/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0352 - val_loss: 0.0653\n", "Epoch 48/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0346 - val_loss: 0.0876\n", "Epoch 49/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0316 - val_loss: 0.0684\n", "Epoch 50/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0322 - val_loss: 0.0825\n", "Epoch 51/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0320 - val_loss: 0.0637\n", "Epoch 52/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0322 - val_loss: 0.0714\n", "Epoch 53/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0343 - val_loss: 0.0830\n", "Epoch 54/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0325 - val_loss: 0.0560\n", "Epoch 55/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0312 - val_loss: 0.0751\n", "Epoch 56/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0295 - val_loss: 0.0779\n", "Epoch 57/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0312 - val_loss: 0.0893\n", "Epoch 58/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0301 - val_loss: 0.0790\n", "Epoch 59/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0325 - val_loss: 0.0802\n", "Epoch 60/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0309 - val_loss: 0.0788\n", "Epoch 61/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0309 - val_loss: 0.0808\n", "Epoch 62/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0318 - val_loss: 0.0847\n", "Epoch 63/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0309 - val_loss: 0.0853\n", "Epoch 64/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0301 - val_loss: 0.0792\n", "Epoch 65/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0323 - val_loss: 0.0772\n", "Epoch 66/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0307 - val_loss: 0.1031\n", "Epoch 67/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0321 - val_loss: 0.0724\n", "Epoch 68/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0291 - val_loss: 0.0741\n", "Epoch 69/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0292 - val_loss: 0.0715\n", "Epoch 70/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0299 - val_loss: 0.0883\n", "Epoch 71/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0326 - val_loss: 0.0799\n", "Epoch 72/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0296 - val_loss: 0.0926\n", "Epoch 73/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0296 - val_loss: 0.0984\n", "Epoch 74/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0295 - val_loss: 0.0942\n", "Epoch 75/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0297 - val_loss: 0.0896\n", "Epoch 76/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0308 - val_loss: 0.0726\n", "Epoch 77/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0306 - val_loss: 0.0913\n", "Epoch 78/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0303 - val_loss: 0.0706\n", "Epoch 79/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0303 - val_loss: 0.0832\n", "Epoch 80/1000\n", "25/25 [==============================] - 0s 5ms/step - loss: 0.0302 - val_loss: 0.0997\n", "Epoch 81/1000\n", "25/25 [==============================] - 0s 6ms/step - loss: 0.0316 - val_loss: 0.0758\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "early_stopping = EarlyStopping(monitor='val_loss', patience=50, restore_best_weights=True)\n", "model.fit(input_train, y_train, epochs=epochs, verbose=1, validation_data=(input_val, y_val), callbacks=[early_stopping])" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "25/25 [==============================] - 0s 2ms/step\n", "7/7 [==============================] - 0s 3ms/step\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_pred_train = model.predict(input_train)\n", "y_pred_val = model.predict(input_val)\n", "\n", "plt.figure(figsize=(18,10))\n", "\n", "plt.subplot(1, 2, 1)\n", "plt.plot(t_train, y_train[:, 0], label='True position (train)')\n", "plt.plot(t_val, y_val[:, 0], label='True position (validation)')\n", "plt.plot(t_train, y_pred_train[:, 0], label='Predicted position (train)')\n", "plt.plot(t_val, y_pred_val[:, 0], label='Predicted position (validation)')\n", "plt.xlabel('Time')\n", "plt.ylabel('Position')\n", "plt.legend()\n", "\n", "plt.subplot(1, 2, 2)\n", "plt.plot(t_train, y_train[:, 1], label='True velocity (train)')\n", "plt.plot(t_val, y_val[:, 1], label='True velocity (validation)')\n", "plt.plot(t_train, y_pred_train[:, 1], label='Predicted velocity (train)')\n", "plt.plot(t_val, y_pred_val[:, 1], label='Predicted velocity (validation)')\n", "plt.xlabel('Time')\n", "plt.ylabel('Velocity')\n", "plt.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Test Model on Other Initial Conditions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Predicting Critical Damping" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "gamma = 1\n", "Ftilde = 0\n", "Omegatilde = 1\n", "\n", "t_span = (0, 20)\n", "t_eval = np.linspace(*t_span, num=1000)\n", "initial_conditions = [2, 2]\n", "\n", "solution = solve_ivp(SpringForce, t_span, initial_conditions, args=(gamma, Ftilde, Omegatilde), t_eval=t_eval, method='RK45')\n", "t_train = solution.t\n", "y_train = solution.y.T" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "validation_split = 0.2\n", "split_index = int((1 - validation_split) * len(t_train))\n", "\n", "t_train, t_val = t_train[:split_index], t_train[split_index:]\n", "y_train, y_val = y_train[:split_index], y_train[split_index:]" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "input_train = np.column_stack((t_train, y_train))\n", "input_train = input_train[:, np.newaxis, :]\n", "\n", "input_val = np.column_stack((t_val, y_val))\n", "input_val = input_val[:, np.newaxis, :]" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "25/25 [==============================] - 0s 3ms/step\n", "7/7 [==============================] - 0s 3ms/step\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_pred_train = model.predict(input_train)\n", "y_pred_val = model.predict(input_val)\n", "\n", "plt.figure(figsize=(18,10))\n", "\n", "plt.subplot(1, 2, 1)\n", "plt.plot(t_train, y_train[:, 0], label='True position (train)')\n", "plt.plot(t_val, y_val[:, 0], label='True position (validation)')\n", "plt.plot(t_train, y_pred_train[:, 0], label='Predicted position (train)')\n", "plt.plot(t_val, y_pred_val[:, 0], label='Predicted position (validation)')\n", "plt.xlabel('Time')\n", "plt.ylabel('Position')\n", "plt.legend()\n", "\n", "plt.subplot(1, 2, 2)\n", "plt.plot(t_train, y_train[:, 1], label='True velocity (train)')\n", "plt.plot(t_val, y_val[:, 1], label='True velocity (validation)')\n", "plt.plot(t_train, y_pred_train[:, 1], label='Predicted velocity (train)')\n", "plt.plot(t_val, y_pred_val[:, 1], label='Predicted velocity (validation)')\n", "plt.xlabel('Time')\n", "plt.ylabel('Velocity')\n", "plt.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Predicting Underdamping" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "gamma = 0.2\n", "Ftilde = 0\n", "Omegatilde = 0.5\n", "\n", "t_span = (0, 20)\n", "t_eval = np.linspace(*t_span, num=1000)\n", "initial_conditions = [2, 2]\n", "\n", "solution = solve_ivp(SpringForce, t_span, initial_conditions, args=(gamma, Ftilde, Omegatilde), t_eval=t_eval, method='RK45')\n", "t_train = solution.t\n", "y_train = solution.y.T" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "validation_split = 0.2\n", "split_index = int((1 - validation_split) * len(t_train))\n", "\n", "t_train, t_val = t_train[:split_index], t_train[split_index:]\n", "y_train, y_val = y_train[:split_index], y_train[split_index:]" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "input_train = np.column_stack((t_train, y_train))\n", "input_train = input_train[:, np.newaxis, :]\n", "\n", "input_val = np.column_stack((t_val, y_val))\n", "input_val = input_val[:, np.newaxis, :]" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "25/25 [==============================] - 0s 2ms/step\n", "7/7 [==============================] - 0s 3ms/step\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_pred_train = model.predict(input_train)\n", "y_pred_val = model.predict(input_val)\n", "\n", "plt.figure(figsize=(18,10))\n", "\n", "plt.subplot(1, 2, 1)\n", "plt.plot(t_train, y_train[:, 0], label='True position (train)')\n", "plt.plot(t_val, y_val[:, 0], label='True position (validation)')\n", "plt.plot(t_train, y_pred_train[:, 0], label='Predicted position (train)')\n", "plt.plot(t_val, y_pred_val[:, 0], label='Predicted position (validation)')\n", "plt.xlabel('Time')\n", "plt.ylabel('Position')\n", "plt.legend()\n", "\n", "plt.subplot(1, 2, 2)\n", "plt.plot(t_train, y_train[:, 1], label='True velocity (train)')\n", "plt.plot(t_val, y_val[:, 1], label='True velocity (validation)')\n", "plt.plot(t_train, y_pred_train[:, 1], label='Predicted velocity (train)')\n", "plt.plot(t_val, y_pred_val[:, 1], label='Predicted velocity (validation)')\n", "plt.xlabel('Time')\n", "plt.ylabel('Velocity')\n", "plt.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is common for neural networks to achieve a high degree of accuracy when modeling physical systems, but it is rare for them to be 100% accurate. The neural network in the provided code was trained on a specific driven oscillation system and later tested on critical and underdamping systems. While the model was able to predict the behavior of the systems with reasonable accuracy, it was not 100% accurate.\n", "\n", "There are several reasons why a neural network may not achieve 100% accuracy when modeling physical systems. One reason is that physical systems can exhibit complex and nonlinear behavior, and it may be challenging to capture all the details of the system in the neural network. Another reason is that the neural network is only as accurate as the data it is trained on. If the training data does not represent the system's behavior accurately, the neural network's performance may suffer.\n", "\n", "In the case of the provided code, the neural network was trained on a specific driven oscillation system, and its accuracy was later tested on critical and underdamping systems. While the network was able to model the behavior of these systems, it was not 100% accurate, possibly due to the differences in the behavior of these systems compared to the driven oscillation system used for training. Additionally, the neural network's accuracy may be affected by the specific hyperparameters chosen, such as the number of hidden layers and the regularization techniques used.\n", "\n", "Overall, while the neural network in the provided code was not 100% accurate in modeling the critical and underdamping systems, it still provided a useful tool for predicting their behavior. With further fine-tuning of the model's hyperparameters and additional training data, the accuracy of the neural network could potentially be improved." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "-----\n", "\n", "Written by Agrim Gupta, Astrophysics & Data Science Major, Michigan State University" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.10" } }, "nbformat": 4, "nbformat_minor": 4 }