Chapter 5.6, Problem 1P

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.

$y\text{'}\text{'}+y=f(t);$ $y(0)=5,$ $y\text{'}(0)=3;$

$f(t)=\{\begin{array}{c}1,0\le t<\pi /2\\ 0,\pi 2\le t<\infty \end{array}$