Add a third spring connected to mass 2 in the coupled system shown in Figure 3. 15 to a wall on the far right. Assume that the masses are the same and the springs are the same.

a. Model this system with a set of first-order differential equations.

b. If the masses are all \(2.0 \mathrm{~kg}\) and the spring constants are all 10. 0 \(\mathrm{N} / \mathrm{m}\), then find the general solution for the system.

c. Move mass 1 to the left (of equilibrium) \(10.0 \mathrm{~cm}\) and mass 2 to the right \(5.0 \mathrm{~cm}\). Let them go. find the solution and plot it as a function of time. Where is each mass at 5. 0 seconds?

d. Model this initial value problem with a set of two second-order differential equations setup the system in the form \(M \ddot{x}=K x\) and solve using the values in part \(b\).

kj my k2 N m k3 llllll illllll llllll llllll x1 x2