The pendulum below is actuated with a servo-motor with a torque u. The angular displacement O...

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The pendulum below is actuated with a servo-motor with a torque u. The angular displacement O is large and the pendulum experiences air resistance force which can be approximated as c and acts at the center of mass of the pendulum. Mg a) Use Newton's second law method to derive the nonlinear equation of motion (8 marks) b) Linearize the equation of motion obtained in (a) about the equilibrium position 0 = 0 (6 marks) c) Determine if the system is stable if M = 0.5 kg, 1 = 55 cm, c = 15 Ns/m, u = 3 Nm. (8 marks) The pendulum below is actuated with a servo-motor with a torque u. The angular displacement O is large and the pendulum experiences air resistance force which can be approximated as c and acts at the center of mass of the pendulum. Mg a) Use Newton's second law method to derive the nonlinear equation of motion (8 marks) b) Linearize the equation of motion obtained in (a) about the equilibrium position 0 = 0 (6 marks) c) Determine if the system is stable if M = 0.5 kg, 1 = 55 cm, c = 15 Ns/m, u = 3 Nm. (8 marks)