Laplace II: Steps, Impulses & Convolution · Superchallenge problem

An undamped oscillator at rest is driven by a square wave of the same period: $y''+y=f(t)$, $y(0)=y'(0)=0$, where $f(t)=1$ on $[0,\pi)$, $-1$ on $[\pi,2\pi)$, $1$ on $[2\pi,3\pi)$, and so on. Find $y(10\pi)$.