Forced pendulum. Consider the forced pendulum equations = -a sin 0 b + cT with a = c = 10, b = 0, and the torque T = a sin desired - k(0 - desired) - 0, with desired = /4, k1 = 2.5 and k = 1. Find a Lyapunov function for the system and use it to provide an estimate of the region of attraction as accurate as possible. Use matlab/mathematica to plot a few trajectories of the system and numerically estimate the actual region of attraction. Check this against your estimate.