(a) Plot the quantity E = 1/2mv2 + 1/2ky2 as a function of time. What do you observe? Is the energy conserved in this case?
(b) Show analytically that dE/dt < 0 for c > 0 while dE/dt > 0 for c < 0.
(c) Plot v vs y (phase plot). Comment on the behavior of the curve in the context of the motion of the spring. Does the graph ever get close to the origin? Why or why not?