Find the transient response of an undamped spring-mass system for \(t>\pi / \omega\) when the mass is subjected to a force 4.19. Find the transient response of an undamped spring-mass system for \(t>\pi / \omega\) when the mass is subjected to a force

\[F(t)= \begin{cases}\frac{F_{0}}{2}(1-\cos \omega t) & \text { for } 0 \leq t \leq \frac{\pi}{\omega} \\ F_{0} & \text { for } t>\frac{\pi}{\omega}\end{cases}\]

Assume that the displacement and velocity of the mass are zero at \(t=0\).