Question

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?

Short answer

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

Step-by-step solution

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

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

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.

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.