Problem 3 (10 points) a) Consider the undamped pendulum, as in Figure 2 with = 1. Create the state- space portrait for the equation of motion in the domain 0 1-1, 1], -4,4) in MATLAB using the quiver command. b) On a separate plot, visualize trajectories in the same domain using ode45. Use the initial conditions (0) = -1+0.5i and 0(0) -4+0.5j, where i and j are integers. Use the interval of integration as t (0,7). Make sure that when you are plotting, you only plot in the domain 0 (-1, 1) and (-4,4). c) Repeat parts a) and b), but with a damped pendulum as in Figure 3. Suppose co/(ml2) = 1. 0 Figure 2: Pendulum without damper Problem 3 (10 points) a) Consider the undamped pendulum, as in Figure 2 with = 1. Create the state- space portrait for the equation of motion in the domain 0 1-1, 1], -4,4) in MATLAB using the quiver command. b) On a separate plot, visualize trajectories in the same domain using ode45. Use the initial conditions (0) = -1+0.5i and 0(0) -4+0.5j, where i and j are integers. Use the interval of integration as t (0,7). Make sure that when you are plotting, you only plot in the domain 0 (-1, 1) and (-4,4). c) Repeat parts a) and b), but with a damped pendulum as in Figure 3. Suppose co/(ml2) = 1. 0 Figure 2: Pendulum without damper