Question: Solve the wave equation given the following boundary conditions.
u(0,t)=0
u(L,t)=0
u(x,0)=0
du/dt|t=0= x(L-x)
Attempt:
ok i'm not gonna write out all the steps because i can't use latex and it will be really messy, but i have
un= [Ancos(nπαt/L) + Bnsin(nπαt/L)]sin(nπx/L)
u(x,t) = Σ un
u(x,0) = ΣAnsin(nπx/L) = 0
Question: Does this make An=0?