4. Consider the Mass-spring system shown in Figure 1. (a) Find the equations of motion for the system, where m, and m2 are the masses of the two K3 objects, k1, k2 and ky are the spring constants of the three springs. In addition, you are given that /1, /2 and 13 are the unstretched displacements of spring 1, spring 2, and spring 3, respectively. Rewrite the differential equations as a system of first-order differential LLLLLLLLLLLL equations, x = Ax + c, where x E R4. (b) What are the equilibrium configurations of the system for m1 = 3, m2 = 9, k1 = 1, k2 = 2, k3 = 0.5, l1 = 1, 12 = 2, l3 = 1? k2 (c) Suppose that the displacement of object 1 from the wall is 1 and its velocity is equal to 1 at t = 0. Additionally, suppose that the displacement of object 2 from the wall is 2 and Figure 1: Mass Spring system for Problem 4 its velocity is equal to -1 at time t = 0. With the parameter values defined in part b), compute and plot the approximate displacements of object 1 and 2 over the time interval [0, 20]