Answer: When the magnitude of tension T is not constant, then a model for the deflection
Chapter 5, Problem 26(choose chapter or problem)
When the magnitude of tension T is not constant, then a model for the deflection curve or shape y(x) assumed by a rotating string is given by . Suppose that 1 x e and that T(x) x2 . (a) If y(1) 0, y(e) 0, and rv2 0.25, show that the critical speeds of angular rotation are and the corresponding deflections are yn(x) c2x1/2 sin(np ln x), n 1, 2, 3, . . . . (b) Use a graphing utility to graph the deflection curves on the interval [1, e] for n 1, 2, 3. Choose c2 1.
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