For problems with so-called harmonic oscillations, given by for example the following differential equation $$ m\frac{d^2x}{dt^2}+\eta\frac{dx}{dt}+x(t)=F(t), $$ where \( F(t) \) is an applied external force acting on the system (often called a driving force), one can use the theory of Fourier transformations to find the solutions of this type of equations.
If one has several driving forces, \( F(t)=\sum_n F_n(t) \), one can find the particular solution to each \( F_n \), \( x_{pn}(t) \), and the particular solution for the entire driving force is then given by a series like $$ \begin{equation} x_p(t)=\sum_nx_{pn}(t). \tag{21} \end{equation} $$