Chapter 4.1, Problem 6E

An external force $F\left(t\right)=2\cos 2t$ is applied to a mass–spring system with $m=1$, $b=0$ and $k=4$, which is initially at rest; i.e., $y\left(0\right)=0$, $y^{\prime }\left(0\right)=0$. Verify that $y\left(t\right)=\frac{1}{2}t\sin 2t$ gives the motion of this spring. What will eventually (as t increases) happen to the spring?