Problem 3 Solve the problem describing the motion of a string of unit length Utt = Couxx 00 u(0, t) = u(1, t) = 0 u(x, 0) = $(x) u. (x, 0) = 1(x) for the data given below. Illustrate the string motion by a graphic representation of a partial sum of the resulting series for various values t. Comparing the graph for f = 0 and the graph of the function (x), decide whether the number of terms in the sum is sufficient. (a) (x) = 0.05 sinnx, v(x) = 0, c =1 (b) (x) =2, c = 1