6. Consider the one dimensional wave equation with boundaryconditions 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 surfaceand enough time snapshots to display the dynamics of thesolution
b) What happens to the solution as t ? ?? Explain your answer inlight of (a) and the physical interpretation of the problem. Does(b) reflect this?
c) Redo parts (a) and (b) for c = 1, L = ?, f(x) = 2 sin 3x, andg(x) = 1 ? x.
