Boundary Values & Fourier Series · Medium problem

A string obeys $u_{tt} = 4u_{xx}$ on $0 < x < \pi$ with fixed ends, starts flat, $u(x,0) = 0$, and is struck so that $u_t(x,0) = \sin 3x$. Find $u\!\left(\dfrac\pi6, \dfrac{\pi}{12}\right)$.