Question

In: Advanced Math

6. Consider the one dimensional wave equation with boundary conditions and initial conditions: PDE : utt...

6. Consider the one dimensional wave equation with boundary conditions and initial conditions:

PDE : utt = c 2 uxx, BC : u(0, t) = u(L, t) = 0, IC : u(x, 0) = f(x), ut(x, 0) = g(x)

a) Suppose c = 1, L = 1, f(x) = 180x 2 (1 − x), and g(x) = 0. Using the first 10 terms in the series, plot the solution surface and enough time snapshots to display the dynamics of the solution

b) What happens to the solution as t → ∞? Explain your answer in light of (a) and the physical interpretation of the problem. Does (b) reflect this?

c) Redo parts (a) and (b) for c = 1, L = π, f(x) = 2 sin 3x, and g(x) = 1 − x.

Solutions

Expert Solution

Colby Messinger answered 1 year ago
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