Laplace Transforms · Superchallenge problem

An undamped oscillator is driven at resonance for exactly one period and then released: $y'' + y = \cos t$ for $0 \le t < 2\pi$ and $y'' + y = 0$ for $t \ge 2\pi$, with $y(0) = y'(0) = 0$. Writing the forcing as $\cos t\,\big(1 - u(t - 2\pi)\big)$, use the Laplace transform to find $y\!\left(\dfrac{5\pi}{2}\right)$.