An object of mass m is hung from the base of an ideal spring that is suspended f

Question

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 Dfrom 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?

The period decreases and the frequency increases.The period increases and the frequency decreases.    The period and frequency remain the same.

(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)?

The period decreases and the frequency increases.The period increases and the frequency decreases.    The period and frequency remain the same.

(d) How does the total energy compare to when the object was released from rest at a displacement 2D?

The energy is greater when given an initial push.The initial push has no effect on the energy.    The energy is smaller when given an initial push.

Explanation / Answer

Part A

Time period and frequency does not depend upon displacement so they remain same.

Part _B

Energy is proportional to square of amplitude so

E2D/E1D = 4/1=4:1

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