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**Find the wave equation U(x,t) of a vibrating string with linear density d, tension p, initial velocity zero, weight L and initial displacement**

U0(x) = a1*sin(2*pi*x/L)+a2*sin(4*pi*x/L).

U0(x) = a1*sin(2*pi*x/L)+a2*sin(4*pi*x/L).

Guys, please help me with this task. I did the following procedure:

The U(x,t) solution must me a sum of sine and cosine functions, like

ΣBn*cos(n*pi*a*t/L)*sin(n*pi*x/L).

Then Bn is found with Bn=∫U0(x)*sin(n*pi*x/L)dx. I'm a little lost with all these substitiution that leads me to big integrals with no solution.