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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 ωn=ckn=cnΠ/L, the displacement of the string for t≥0 is
y(x,t) = n-1∑∞(Ancosωnt+Bnsinωnt)sinknx
(a) Which sets of coefficients Aodd, Aeven, Bodd, and Beven 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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