Consider a stationary inclined plane ramp with a fixed angle 6, with three blocks with equal masses M attached by a spring of constant k and a string over a fixed pulley at the top of the ramp, as shown below. The positions of the blocks are described by the distances r(t) (the distance from the pulley to the higher block on the ramp) and y(t) (the extension of the spring), as shown. The system is in a uniform graviational field of acceleration g. The unstretched length of the spring is 0, and the pulley is massless. 0000000 (a) [12 points] Find the Lagrangian and the equations of motion of the system. (b) [20 points] The two blocks on the ramp are released from rest at the top with a = y = 0 at time t = 0. Find the motions of the blocks as a function of time. %3D (c) [8 points] The choice 0 = 30 degrees has a special significance, which should be apparent in the results of part (b). What is it?