Consider a pendulum consisting of a mass M on a thin (nearly massless) rod with length...

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Consider a pendulum consisting of a mass M on a thin (nearly massless) rod with length L. An input torque 7 is applied at the pivot point of the pendulum. The angle 0 measures the deflection of the pendulum away from the vertical. L M (a) Starting from a free-body diagram, obtain the equation of motion of the system (hint: J ML² is the mass moment of inertia of the pendulum about its pivot point). (b) Put the ODE into the state dynamics form i = f(x, u). = (c) Taking the parameter values M = 0.2 kg, L = 0.5 m, g = 9.81 m/s² and input (t) = 0.1 sint, obtain a plot of the response (t) for 0 <t <10 given initial conditions (0) = /6 rad, ė(0) = =-1 rad/s. Submit your plot plus the source code of the .m function you used. Consider a pendulum consisting of a mass M on a thin (nearly massless) rod with length L. An input torque 7 is applied at the pivot point of the pendulum. The angle 0 measures the deflection of the pendulum away from the vertical. L M (a) Starting from a free-body diagram, obtain the equation of motion of the system (hint: J ML² is the mass moment of inertia of the pendulum about its pivot point). (b) Put the ODE into the state dynamics form i = f(x, u). = (c) Taking the parameter values M = 0.2 kg, L = 0.5 m, g = 9.81 m/s² and input (t) = 0.1 sint, obtain a plot of the response (t) for 0 <t <10 given initial conditions (0) = /6 rad, ė(0) = =-1 rad/s. Submit your plot plus the source code of the .m function you used.