An oscillation is a physical phenomenon characterized by the fact that the configuration of a physical system repeats (or almost repeats) itself over and over again. Simple harmonic oscillations are a special case of this. An oscillation is simple harmonic if the period (the time for one cycle) does not depend on the amplitude (the maximum displacement from equilibrium.)

In the following set, identify the oscillation that are simple harmonic, the ones that are approximately simple harmonic and the ones that are not simple harmonic.

1. The pendulum in a grandfather clock
2. A boat in water pushed down and released
3. A child on a swing
4. A mass hanging from a spring
5. A ping-pong ball bouncing on the floor

Estimate the period of a basketball, dropped from a height of one meter and allowed to bounce on a hard floor.

Is this oscillation simple harmonic?

Consider a mass on a spring, oscillating under the influence of a non-conservative retarding force, such as air drag. How would the retarding force affect the period of the oscillations? In a sentence or two, justify your answer.

When you push a child on a swing, your action is most effective when your pushes are timed to coincide with the natural frequency of the motion. You are swinging a 30 kg child on a swing suspended from 5 meter cables.

Estimate the optimum time interval between your pushes.

Repeat the estimate for a 15 kg child.