The Wronskian & Variation of Parameters · Superchallenge problem

A resting oscillator $y''+y=f(t)$, $y(0)=y'(0)=0$, receives a single half-wave push: $f(t)=\sin t$ for $0\le t\le\pi$ and $f(t)=0$ afterwards. Find the amplitude of the free oscillation for $t>\pi$.