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

Chapter 10, Problem 4

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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). G b. Plot u( x, t) versus x for 0 x 10 and for several values of t between t = 0 and t = 20. G c. Plot u( x, t) versus t for 0 t 20 and for several values of x. G 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. f ( x) = 0 0 x L/2 1 1, L/2 1 < x < L/2 + 1 (assume L > 2), 0, L/2 + 1 x 1 Consider an elastic string of length L whose ends are held fixed. The string is set in motion from its equilibrium position with an initial velocity ut ( x, 0) = g( x).