4) Consider the damped wave equation on a square membrane O S S L and 0 yL u(t,0, )0u(t, L, y) a(t, x, 0)-0 u(t, x, L) a(0,x, y) = 0 ue(0,x,y) = 102(L-z)y(y-L) where c>0 is the wave speed and b >0 is the damping parameter. As- sume b is small enough that all modes are underdamped. Find the solution to this problem (use Mathematica to find a formula for the coefficients). Suppose that b = 0.1, c = 2, and L = 1 . Use Mathematica to plot the sum of 100 terms of this series at times 0, 0.5, 1, 15, and 2. 4) Consider the damped wave equation on a square membrane O S S L and 0 yL u(t,0, )0u(t, L, y) a(t, x, 0)-0 u(t, x, L) a(0,x, y) = 0 ue(0,x,y) = 102(L-z)y(y-L) where c>0 is the wave speed and b >0 is the damping parameter. As- sume b is small enough that all modes are underdamped. Find the solution to this problem (use Mathematica to find a formula for the coefficients). Suppose that b = 0.1, c = 2, and L = 1 . Use Mathematica to plot the sum of 100 terms of this series at times 0, 0.5, 1, 15, and 2