Solved: (a) Suppose two identical pendulums are coupled by

Chapter 7, Problem 7.1.338

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(a) Suppose two identical pendulums are coupled by means of a spring with constant k. See Figure 7.R.12. Under the same assumptions made in the discussion preceding Example 3 in Section 7.6, it can be shown that when the displacement angles u1(t) and u2(t) are small, the system of linear differential equations describing the motion is Use the Laplace transform to solve the system when u1(0) u0, u1(0) 0, u2(0) c0, u2(0) 0, where u0 and c0 constants. For convenience let v2 gl, K km. (b) Use the solution in part (a) to discuss the motion of the coupled pendulums in the special case when 2the initial conditions are u1(0) u0, u1 (0) 0, u2(0) u0, u2 (0) 0. When the initial conditions are u1(0) u0, u1 (0) 0, u2(0) u0, u2 (0) 0.