Use the method of variation of parameters to obtain the general solution of Equation (5.1) and show that it can be written in the form of the convolution integral, Equation (5.25).

\(\ddot{x}+2 \zeta \omega_n \dot{x}+\omega_n^2 x=\frac{F_{\mathrm{eq}}(t)}{m_{\mathrm{eq}}} \tag{5.1}\)

\(x(t)=\frac{1}{m_{\mathrm{eq}} \omega_d} \int_0^t F(\tau) e^{-\zeta \omega_{\mathrm{m}}(t-\tau)} \sin \omega_d(t-\tau) d \tau \tag{5.25}\)