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Found in: Page 472

### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

# Is a bouncing ball an example of simple harmonic motion? Is the daily movement of a student from home to school and back simple harmonic motion? Why or why not?

Although they are both periodic motion, neither are examples of simple harmonic motion.

See the step by step solution

## Step 1: Simple Harmonic motion

Particle in Simple Harmonic Motion If a particle is subject to a force of the form of Hooke’s law $F=-kx$, the particle exhibits simple harmonic motion. Its position is described by

$x\left(t\right)=A\mathrm{cos}\left(\omega t+\varphi \right)$

Where A is the amplitude of the motion, $\omega$ is the angular frequency, and $\varphi$ is the phase constant. The value of $\varphi$ depends on the initial position and initial velocity of the particle.

## Step 2: Explain the reasoning

• Although they are both periodic motion, neither are examples of simple harmonic motion.
• In neither case is the acceleration proportional to the displacement from an equilibrium position. Neither motion is so smooth as SHM.
• The ball’s acceleration is very large when it is in contact with the floor, and the student’s when the dismissal bell rings.

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