Expressing the displacement of a string in terms of the normal modes

catpants

1. The problem statement, all variables and given/known data
http://img85.imageshack.us/img85/8230/problem21.png

Basically, I just need help interpreting the problem in order to get started. (And then I will probably need help with the rest of the problem, once I understand what it is I'm trying to do, lol.)

So they say "by expressing the displacement of the string in terms of the normal modes" which brings to mind expressing any sort of function in terms of sines and cosines: Fourier series. I might just be stupid, but what exactly am I trying to express in terms of normal modes here?

Thanks!