Chapter 3, Problem 3.35P

To determine

The response of a linear oscillator to the forcing function, $\frac{F\left(t\right)}{m}=\{\begin{array}{cc}0& t<0\\ a\sin \omega t& 0<t<\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$\omega $}\right.\\ 0& t>\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$\omega $}\right.\end{array}$ .