Fig. 1 Fig. 2 2k 21 ne L/6 3k Fig. 3.a Fig. 3.b 1) Figure I...

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Fig. 1 Fig. 2 2k 21 ne L/6 3k Fig. 3.a Fig. 3.b 1) Figure I shows a drive train with a spur-gear pair. The first shaft turns N times faster than the second shaft. Develop a model of the system including the elasticity of the second shaft. Assume the first shaft is rigid, and neglect the gear and shaft masses. The input is the applied torque Th. The outputs are the angles & and 6. 2) Assume a small oscillating angle around θ=0, derive the linearized equation of motion of the pendulum shown in figure 2. The input is 0) and the output is &. The motion is in the horizontal plane, and the system started from zero initial conditions. 0)-10-Cos 2x i) m Ans. 270+629-9+09a Sin(Zrt)-9Cos(2π t) 3) Determine DOF and equations of motion of the systems shown in figures 3.a and 3.b. Assume small oscillating angke around -0, and represent equations of motion in state-space form in problem 3.b. Hint: in 3.a, the tension in the cable at the right pulley does not equal to 2mg. D.17

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