13) is given as:
\[ \frac{d^2x}{dt^2} + 2\zeta\omega_n\frac{dx}{dt} + \omega_n^2x = \frac{F(t)}{m} \]
To derive equation (24.15), we need to assume that the forcing function \( F(t) \) is a sinusoidal function of the form \( F(t) = F_0\cos(\omega t) \), where \(
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