2. Figure 2 shows a system with two masses of which the origins are set up for the springs of k, k2, and kg to be unstretched. The system is excited by the base motion of x,(t). (a) By drawing the FBDs of the two masses and applying the Newton's 2nd Law of Motion, find a matrix equation of motion. (b) Find the undamped, natural frequencies and the corresponding mode shapes of the system for the given system parameters of m = 4m = 16 kg, c = c = 20 Ns/m, and k = k = k3 = 200 kN/m. (c) Can the damping matrix be diagonalized? Explain why or why not. k mi A CI X1 k m2 Figure 2: 2-DOF Damped System. Massless plate X2 k3