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