Two masses ml and m2, each connected by two springs of stiffness k, are connected by a rigid massless horizontal rod of length /as shown in Fig. (a) Derive the equations of motion of the system in terms of the vertical displacement of the C.G. of the system, x(), and the rotation about the C.G. of the system, e(t). (b) Find the natural frequencies of vibration of the system for ml = 50 kg, m2 = 200 kg, and k= 1000 N/m. Assume /= I m Figure: (0) m2 x() Rigid, massless rod 00000000 00000000 T.