The double pendulum is shown in Figure 2.1. Parameters for this double pendulum are 4 = 0.2 m, l = 0.4 m, m = 0.02 kg, m = 0.04 kg. 4 3/ m Figure 2.1: Double pendulum Requirements for Question 2: (a) Derive the differential equations of motion for the double pendulum using the coordinates and and assume small angles. (b) Derive the differential equations of motion for the double pendulum coordinates X and x and assuming small amplitudes. (8 marks) using the (4 marks) (c) Find the response of the free vibration of the system with 8 (0) = -0.57 rad, (0) = 0 rad/s, 0 (0) = 1.57 rad, 0 (0) = 0 rad/s x (0) = -0.1 m, x (0) = 0 m/s, x (0) = 0.2 m, x (0) = 0 m/s Plot the response figures and give some comments. (8 marks) 8 m