4 B, Triple pendulum (20 points) am a m (6 pts) m A triple pendulum consists of masses am, m, and m suspended to each other in a line by three massless rods of length a pictured above. The whole set-up is suspended from a stationary pivot. Throughout this problem, you may assume that the displacements of the masses from equilibrium are small. Using the generalized coordinates shown, note that the positions of the masses are x = a sin = Y = acos Y2 = a(sin + sin 2) x3 = a(cos + cos 02) 93 = a(sin + sin 2+ sin 03) a(cos + cos 2+ cos 03) (2) 2 1. Show that for small oscillations, 01, 02, 031, the Kinetic energy of the system is given by T ma [0(2+ a) +20 +0 +400 + 20203 + 20103] Hence, write down the M matrix. 5 pts (3) 2. Show that for small oscillations, 01, 02, 03