Assume that a rotor has inertia, Jm = 0.01 kg m2 and friction coefficient, b = 0

Question

Assume that a rotor has inertia, Jm = 0.01 kg m2 and friction coefficient, b = 0.001 N m sec. The free-body diagram for the rotor is shown in Fig 1, Left. This figure shows the positive direction and the two applied torques, T = kava and b theta m, where Ka = 0.002 N m and va is the input. Theta m and va are measured in radians. Find equation of motion for the rotor. Find the transfer function between the applied input va and the rotor speed theta m. Find the transfer function between theta r and theta m if the input is given as va = K (theta r - theta m) , where K is the constant coefficient and has no units, and theta r is the constant angle and also measured in radians. Find the total response of the rotor using the input va = K1 theta r - K2 theta m with K1 = 0.5, K2 = 0.2 and theta r = 0.4 rad, and identify transient (dissipating), steady-state, free and forced responses if they exist. Is the rotor's motion stable and why?. Is it possible to express theta m in terms of only theta m, so that such an expression does not include time, t explicitly?

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