(a) Suppose two identical pendulums are coupled by means of a spring withconstantk. See

Chapter 4, Problem 45

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(a) Suppose two identical pendulums are coupled by means of a spring withconstantk. See FIGURE 4.R.10. Underthe same assumptions made in the discussion preceding Example 3, in Section 4.6 it can be shown that when the displacement angles 81(t) and 82(t) are small the system of linear differential equations describing the motion is Use the Laplace transform to solve the system where 81(0) = 80, 8i (0) = 0, 82(0) = 1{10, 82(0) = 0, where 80 and1{10 are constants. For convenience, let w2 = gll, K = klm. (b) Use the solution in part (a) to discuss the motion of the coupled pendulums in the special case when the initial conditionsare61(0) = 80, 8i(O) = 0, 82(0) = 80, 82(0) = 0. When the initial conditions are lli(O) = 80, OHO) = 0, 82(0) = -80, 82(0) = 0. m FIGURE 4.R.10 Coupled pendulums in 45