In all of the following exercises, assume 0 < << 1. In Exercises 14.9.114.9.7, use the
Chapter 14, Problem 14.9.5(choose chapter or problem)
In all of the following exercises, assume 0 < << 1. In Exercises 14.9.114.9.7, use the method of multiple scales to obtain equations for the amplitude and phase.A linearized pendulum with varying length L can be shown to satisfy the following equation: d2u dt2 + g Lu = 2 1 L dL dt du dt . Note that the right-hand side is not zero. Suppose L is a slowly varying length L = L(t). Use the method of multiple scales to obtain a solution valid when t = O(1). (Hint: 1 L dL dt = L dL dT , where T = t.)
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