The displacement field u(x,t) of a propagating wave in one dimension is governed by the equation:
utt = uxx . (1)
Consider a bar of length L = 1 which is initially at rest:
u(x,t) = 0, t ≤ 0, 0 ≤ x ≤ L. (2)
The bar is excited at its left end, i.e., someone starts to move the left end of the bar according to:
(
1−cos(2t) 0 ≤ t ≤ π
u(0,t) = f(t) = (3)
0 otherwise.
The right end of the bar is pinned, i.e.,
u(L,t) = 0, (4)
so that incoming waves will be reflected. Use an explicit finite-difference scheme to solve this problem and plot the solution at t = 20,40,60,80,100.
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