# Elastic Collisions and Harmonic Motion

## Homework Statement

A ball is dropped from a height of 10 meters onto a hard surface so that the collision at the surface may be assumed elastic. Under such conditions the motion of the ball is
(A) simple harmonic with a period of about 1.4 s
(B) simple harmonic with a period of about 2.8 s
(C) simple harmonic with an amplitude of 5 m
(D) periodic with a period of about 2.8 s but not simple harmonic
(E) motion with constant momentum

## The Attempt at a Solution

I would assume that since its an elastic collision, that it would engage in simple harmonic motion, but the answer is D so evidently that is not the case. Anyone care to explain?

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You must have a definition of Harmonic motion somewhere in you textbook.It really isn't hard to find out if that definition does apply.

the acceleration is not directly proportional to the displacement but a constant acceleration (assume there is no air resistance)
there is no equilibrium position between the extreme ends... (as well as force= 0)
and the direction is downward besides at the pt where the ball rebounces....
it is periodic motion, since the collision is elastic .i.e. energy(KE) is conserved.
by s=ut+1/2at^2
s=5t^2
t = sqrt 2=1.41 , representing the time for "half motion"
T=1.41*2=2.82 s

the acceleration is not directly proportional to the displacement but a constant acceleration
so it isn't harmonic motion. The acceleration isn't constant when the ball bounces
of course. If "movement with constant acceleration" was a question, I'd have to