Question

# 4. Find the solution of the vibrating string problem for each initial condition:

121uxx = utt, 0 < x <

π,

u(0,t) = 0, u(π,t) = 0, t > 0.

(a) u(x,0) = 6sin(2x) + sin(5x) − 9sin(12x), ut(x,0) = 0.

(b) u(x,0) = 0, ut(x,0) = 3.

(c) u(x,0) = 6sin(2x) + sin(5x) − 9sin(12x), ut(x,0) = 3.

Is your answer for (c) simply the sum of answers to (a) and (b)?

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