A plate cam drives a reciprocating roller follower through distance L = 1.25 in with parabolic motion in 120◦ of cam rotation, dwells for 30◦, and returns with cycloidal motion in 120◦, followed by a dwell for the remaining cam angle. The external load on the follower is F14 = 36 lb during the rise, and is zero during the dwells and the return. In the notation of Fig. 6.41, R = 3 in, r = 1 in, lB = 6 in, lC = 8 in, and k = 150 lb/in. The spring is assembled with a preload of 37.5 lb when the follower is at the bottom of its stroke. The weight of the follower is 1.8 lb and the cam velocity is 140 rad/s. Assuming no friction, plot the displacement, the torque exerted on the cam by the shaft, and the radial component of the contact force exerted by the roller against the cam surface for one complete cycle of motion.