.1 mm 2; ' Consider initial value problem for the undamped nonlinear pendulum 6\" + sin(6) = 0 with initial conditions 6(0) = 60, 6'(0) = am. We dene the 'total energy' to be the sum of the 'kinetic' and 'potential' energy: E[6,w] = $012 + 1 cos(6). a) Show that E[6(t), 6'(t)] = E[60,w0] for solutions to the initial value problem. b) Determine the threshold E1 such that if E[60,w0] E1 the solution is unbounded. [Hintz The boundedness is determined by the minimum angular speed, |6|' , which is obtained either when the angle is 6 = 7r + 27rk for an integer k or the maximum possible angle] 0) Draw the phase portrait for three solutions, one with energy greater than E1, one with energy equal to E1 and one with energy less than E1