Originally Posted by

**harkapobi** Hi,

i have this question:

$\displaystyle u_{tt}$ = $\displaystyle c^2u_{xx}$

Find u(x,t) the deviateion from equilibrium for a stretched string fixed at its ends x=0 and x= pi. Initial conditions u(x,0)=alpha(sin(x) + 0.2sin(3x)), $\displaystyle u_{t}$(x,0)= 0.

I know to use seperation of variables u(x, t) = F(x)G(t) giving me two ode's

G"(t) - sG(t) = 0

F"(x) - (s/$\displaystyle c^2$)F(x) = 0 where s is a constant.

This gives the solutions:

F(x) = A1sin(nx)

G(t) = A2cos(nct) + B2sin(nct)

Now i'm stuck, how do I use the boundary and initial conditions to solve this? I know it has something to do with the fourier series?

Please help,

Katy