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Q11CQ

Expert-verifiedFound in: Page 472

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.

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.

- 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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