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# Solutions of the wave equation

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A string of length L is fixed at both ends. The speed of waves on the string is c. The string is initially displaced a distance h uniformly along its length, and is released from rest at t=0. (The string initially has a very large slope at x=0 and x=L; assume the slope is infinite.)

For w_n=ckn=cn*pi/L, the displacement of the string for t>=0 the displacement is

Sum(A_n*cos(wt) + B_n*sin(wt))

(a) Which sets of coefficients A_odd, A_even, B_odd, and B_even are zero? (b) Determine the values of the nonzero coefficients. Express your results only in terms of c, L, h, and n.

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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

A string of length L is fixed at both ends. The speed of waves on the string is c. The string is initially ...

#### Solution Summary

The attached file shows how to analyze a general solution of the wave equation using Fourier analysis.

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