For a string with fixed ends, which normal modes are missing?

[snickersnee]

Homework Statement

Here's the problem. I was able to find the a_n and b_n values, my question is mainly on part (c), how do I find which modes are missing? The function is odd, so even modes should disappear, but cos(n*pi) doesn't disappear, it's either +1 or -1. I'd greatly appreciate any help.

[/B]

Homework Equations

b_n = 0 because released from rest[/B]

The Attempt at a Solution

[/B]

 

[RUber]

When it says fixed ends, are we to assume that at x = 0 and x = L, the ends are fixed at $\xi(0,t) = \xi(L,t) = 0$?
If so, then you should be able to say something about $\xi( L/2,t)$.

Using your equation for a_n, break that into two integrals, one from 0 to L/2 and one from L/2 to L. Then enforce an appropriate matching condition for $\xi(L/2,t)$ and $\xi_t(L/2,t)$