Question

Find the solution u(x,t) for the wave problem on a string of length L=π, with c^2=1 and conditions given by:

u(0,t)=0, u(π,t)=0, t>0
u(x,0)=0, ∂u/∂t_(t=0)=sin⁡x, 0<x<π

Answer 1

well, if u(x,t) = cos(kx-wt) then
∂u/∂t = w sin(kx-wt)
see what you can do with that.