Figure P2.22 shows two pendulums suspended from frictionless pivots and connected at their midpoints by a spring [1]. Assume that each pendulum can be represented by a mass M at the end of a mass less bar of length L. Also assume that the displacement is small and linear approximations can be used for sin θ and cos θ. The spring located in the middle of the bars is unstretched when θ1 = θ2. The input force is represented by f(t), which influences the left-hand bar only.
(a) Obtain the equations of motion, and sketch a block diagram for them.
(b) Determine the transfer function T(s) = θ1(s)/F(s).
(c) Sketch the location of the poles and zeros of T(s) on the s-plane.

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0 L/2 FIGURE P2.22 The bars aro each of length L and the spring is located at L/2