i have this question:
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)), (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/ )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?