Chapter 4.6, Problem 17P

Consider the forced but undamped system described by the initial value problem

$y"+y=3\cos wt$,      $y\left(0\right)=0$,      $y\text{'}\left(0\right)=0$.

Find the solution $y(t)$ for $w\ne 1$.

Plot the solution $y(t)$ versus $t$ for $w=0.7$, $w=0.8$ and $w=0.9$. Describe how the response $y(t)$ changes as $w$ varies in this interval. What happens as $w$ takes on values closer and closer to $1$? Note that the natural frequency of the unforced system is $w_0=1$.