
Concept explainers
Is a vertically bouncing ball an example of oscillatory motion? Of

Whether a vertically bouncing ball an example of oscillatory and simple harmonic motion.
Answer to Problem 1FTD
A vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.
Explanation of Solution
An oscillatory motion is one in which a system goes back and forth an equilibrium point. A simple harmonic motion is one in which the restoring force is proportional to the displacement of the system.
When a ball is made to move in the vertical direction, the ball bounces of the ground and comes back to the ground. This happens in the same way as an oscillatory motion. The ball moves to and fro with respect to the ground and ergo, the vertically bouncing ball qualifies as an oscillatory system.
For a simple harmonic oscillator the restoring force acting on the material is proportional to the displacement. When the ball bounces vertically with low amplitude the ball will have a restoring force that is proportional to the amplitude which will keep it bouncing. Therefore, the bouncing ball will qualify as a simple harmonic oscillator when the amplitude of bouncing is low.
Conclusion:
Therefore, a vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.
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