Now solved: Consider an elastic string of length L whose ends are held fixed. The string

Chapter 10, Problem 1

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Consider an elastic string of length L whose ends are held fixed. The string is set in motion with no initial velocity from an initial position u(x, 0) = f(x). In each of 1 through 4 carry out the following steps. Let L = 10 and a = 1 in parts (b) through (d). (a) Find the displacement u(x, t) for the given initial position f(x). (b) Plot u(x, t) versus x for 0 x 10 and for several values of t between t = 0 and t = 20. (c) Plot u(x, t) versus t for 0 t 20 and for several values of x. (d) Construct an animation of the solution in time for at least one period. (e) Describe the motion of the string in a few sentences.(x) =2x/L, 0 x L/2,2(L x)/L, L/2 < x L

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