On a smooth horizontal surface, a mass of m1 kg is

QUESTION:

On a smooth horizontal surface, a mass of m1 kg is attached to a fixed wall by a spring with spring constant k1 N/m. Another mass of m2 kg is attached to the first object by a spring with spring constant k2 N/m. The objects are aligned horizontally so that the springs are their natural lengths. As we showed in Section 5.6, this coupled mass–spring system is governed by the system of differential equations Let’s assume that m1=m2=1,k1=3, and k2=2. If both objects are displaced 1 m to the right of their equilibrium positions (compare Figure 5.26, page 285) and then released, determine the equations of motion for the objects as follows: Figure 5.26 Coupled system at equilibrium(a) Show that x(t) satisfies the equation (b) Find a general solution x(t) to (36).(c) Substitute x(t) back into (34) to obtain a general solution for y(t).(d) Use the initial conditions to determine the solutions,x(t) and y(t) which are the equations of motion.