If a vibrating string satisfying (4.4.1)(4.4.3) is initially unperturbed, f(x) = 0, with
Chapter 4, Problem 4.4.8(choose chapter or problem)
If a vibrating string satisfying (4.4.1)(4.4.3) is initially unperturbed, f(x) = 0, with the initial velocity given, show that u(x, t) = 1 2c x+ct xct G(x) dx, where G(x) is the odd-periodic extension of g(x). [Hints: 1. For all x, G(x) = n=1 Bn nc L sin nx L . 2. sin a sin b = 1 2 [cos(a b) cos(a + b)].] See the comment after Exercise 4.4.7.
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