Chapter 4.6, Problem 18P

Consider the vibrating system described by the initial value problem

$y"+y=3\cos wt$,          $y\left(0\right)=1$,          $y\text{'}\left(0\right)=1$.

Find the solution for $w\ne 1$.

Plot the solution $y(t)$ versus $t$ for $w=0.7$, $w=0.8$ and $w=0.9$. Compare the results with those of Problem $17$, that is, describe the effect of the nonzero initial conditions.