Consider the Mass-spring system shown in Figure 1. (a) Find the equations of motion for the system, where my and m2 are the masses of the two objects, k, k2 and k3 are the spring constants of the three springs. In addition, you are given that 1, 12 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 equations, x= Ax+c, where xER. (b) What are the equilibrium configurations of the system for m3, m = 9, k=1, k= 2, ks = 0.5, 1, 122, 3 = 1? (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 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]. = k M k m k3 www.my m2 Figure 1: Mass Spring system for Problem 4