PROBLEM 4 The system consists of two point masses m and 2m attached to a massless rigid rod which is supported by two identical springs of stiffness k, as sketched in the figure below. The right-hand mass is acted upon by a vertical force F(t). Assume that no gravity acts on the system and that the springs are undeformed when the rod is horizontal (with respect to the ground) and unloaded. Show that for small vertical motions in the plane of the sketch, the equations of motion for the system are given by 3m 0 Ye 2k Ye 1 [0 %mfz} {9}'_[_% % - L F(t), where y.(t) is the vertical displacement of the system's centre of mass, and (t) is the angle of the rod, both defined with respect to the unloaded horizontal equilibrium position of the system. m