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Consider an elastic string of length L
==
10 whose ends are held fixed. The string is set in
motion from its equilibrium position with an initial velocity ut(x, 0) = g(x).
In the following problems, let a = 1 and find the displacement u(x, t) for the given initial
velocity g(x).
4x/L,
0 < x <L/4,
6a. f(x) = 1,
L/4 < x < 3L/4,
| 4(L-x)/L,
4(L – x)/L,
3L/4 ≤ x ≤ L.

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