Year 12s: what will be the first way you research your future options? >>

PDE's-Waves on a String HELP! +rep!

The Question:

The ends x = 0 and x = L of a stretched string are fixed. The point
p (0 < p < L) is drawn aside a distance h and, at the instant t = 0,
the string is released from rest. Thus
y(x, 0) = hx/p , 0<=x<p,
=h(L−x)/(L−p) , p< x<=L
and dy/dt(x, 0) = 0. Use separation of variables and Fourier series to find
y(x, t).

My Attempt
y(x,t)=F(x)G(t)
so c^2F''(x)/F(x)=G''(t)/G(t)=-w^2

F''=(-w^2/c^2)F, and G''=-w^2G

y(0,t)=y(L,t)=0 for all t>0

I think I need to find y(x,0) as a fourier sine series, but when I tried to find an for it I got (2h/Lp)[(n(p-L)sin(np)-cos(Ln)+cos(np))/n^2] + (h/(L-p))[(npsin(np)+cos(np)-1)/n^2] which seems wrong

I have no idea how to answer this question, can anyone outline the method I should use?

thanks xxx

anyone?