In the hanging pendulum system shown, mass m is attached to a rigid rod of length I. The torsional damper shown applies a moment opposing the swinging of the rod such that M--cl . a. Find the exact equation of motion. b. Linearize the equation of motion for small c. What are , , and dud? d. Solve the linearized equation of motion for (t), with initial conditions 4. 6(0)-80 and (0)=Bo. Assume 1 = 2.5 m, m-1 kg, c,-2 N. m. sec/rad, G) = 10 and ,-0. Use MatLab to plot (t) from part d) for t on [0, 15] seconds. Make sure the abscissa and ordinate are appropriately labeled and show the correct units. Print your MatLab script and the plot and include it with the assignment. e