Question

Here's another oscillating system: a perfect Superball bouncing straight up and down. Assume this ball loses no energy upon its rebound from the ground. It'll just keep going up and down forever. I can even find the period...just do the how-long-to-fall-from-a-height-of-h kinematics problem from Week 1, and double it.

Not all oscillating systems are simple harmonic oscillators, however. This Superball oscillator is not. Your job in this essay is to explain why it is not.

Answer 1

The ball does not experience a restoring force that is proportional to its displaced position while in the air. The force of gravity is constant, not proportional to height (for practical purposes).

moves up and down the length of the channel with an oscillation frequency that depends on the ball's moment of inertia. For this vertical channel the introduction of a tangential coefficient of restitution produces motion that is similar to both a damped harmonic oscillator and a falling body.