An object of mass m is hung from the base of an ideal spring that is suspended from the ceiling. The spring has a spring constant k. The object is pulled down a distance D from equilibrium and released. Later, the same system is set oscillating by pulling the object down a distance 2D from equilibrium and then releasing it.
(a) How do the period and frequency of oscillation change when the initial displacement is increased from D to 2D?
(b) How does the total energy of oscillation change when the initial displacement is increased from D to 2D? Give the answer as a numerical ratio.
(c) The mass-spring system is set into oscillation a third time. This time the object is pulled down a distance of 2D and then given a push downward some more, so that it has an initial speed vi downward. How do the period and frequency of oscillation compare to those you found in part (a)?
(d) How does the total energy compare to when the object was released from rest at a displacement 2D?