Nonhomogeneous Equations & Resonance · Superchallenge problem

A mass on a spring with $y''+y=f(t)$ starts at rest, $y(0)=y'(0)=0$. It is pushed with $f(t)=\cos t$ for $0\le t\le\pi$ and then released: $f(t)=0$ for $t>\pi$ ($y$ and $y'$ are continuous at $t=\pi$). For $t>\pi$ the motion is $y=R\cos(t-\varphi)$ with $R>0$. Find $R$.