Quote by Logistics
So I get this ?
z = a  x = a*sinw(Ly) / sinwL
dz/dy = w*acosw(Ly) / sinwL
d^2z/dy^2 = w^2*asinw(Ly) / sinwL
= w^2 * 2
If this is what you were reffering to, what happens now ?

Where did the *2 come from? You mean *z. So
d^2z/dy^2 + w^2*z = 0
Compare this to your DE and identify omega. Put your expression for z into the defining equation for z and solve it for x.