Chapter 5.6, Problem 10P

In each of Problems $1$ through $13$, find the solutions of the given initial value problem. Draw the graphs of the solution and of the forcing function; explain how they are related.

$y\text{'}\text{'}+y\text{'}+1.25y=g(t);$ $y(0)=0,$ $y\text{'}(0)=0;$

$g(t)=\{\begin{array}{c}\sin t,\\ 0,\end{array}\begin{array}{c}0\le t<\pi \\ t\ge \pi \end{array}$