Boundary Values & Fourier Series · Superchallenge problem

A rod $0 \le x \le \pi$ with ends held at $0$ is heated by a periodic source: $u_t = u_{xx} + \sin 3x\cos 2t$, with $u(x, 0) = 0$. After transients die out, $u\!\left(\dfrac\pi2, t\right)$ oscillates sinusoidally. Find the amplitude of that oscillation.