Laplace II: Steps, Impulses & Convolution · Challenge problem

A spring at rest is pushed by a force that grows linearly and is then cut off: $y''+y=f(t)$, $y(0)=y'(0)=0$, where $f(t)=t$ for $0\le t<\pi$ and $f(t)=0$ for $t\ge\pi$. Use the Laplace transform to find $y(2\pi)$.