# Simple Harmonic Motion

Learn.

Simple harmonic motion (SHM) is a unique type of motion. It occurs when an object is oscillating about a fixed point. The force maintaining this motion (known as the restoring force) applies a force in the opposite direction to the displacement of the object. This means every time it moves away from the origin a force is pushing it back to the origin, this makes it over shoot and go past the origin in the opposite direction. This allows this motion to repeat – when graphed the displacement against time a sine function is present hence we say it is sinusoidal motion.

An example of simple harmonic motion is a mass bobbing up and down on a spring. When it is moving down, pulled by gravity, the spring stretches. Eventually it reaches a point where the upward force from the spring exceeds the downward pull of gravity so the mass goes up compressing the spring. Eventually the downward pull of gravity will counteract its upward motion making the spring fall down. Each time this occurs, the spring is oscillating up and down about a fixed point.

This motion can be treated as a wave and described the same way as we did in the mechanical wave model.

Simple harmonic motion can be modeled with this wave function.

The point of equilibrium (where displacement is 0) is the point the object is oscillating about. The crest’s occur when the object is stationary hence we call it the turning points and the amplitude is the maximum displacement from the origin.

T = 1/f

Another way to describe a wave is using the period (T). This is a measure of how long it takes one revolution to pass by. Which is given by the reciprocal of the frequency.

Master.

This mastery section is designed to improve research skills, as such, these will not be exam style questions in this section. If marks are given, the question is an exam style question.

Question 1

Research another example of simple harmonic motion, will this system remain in simple harmonic motion forever, if not, why?

Question 2

A child is being pushed on a swing, they keep on getting higher and higher by swinging there legs back and forth. Explain why this is the case mentioning restoring force and simple harmonic motion. [5 marks]

Question 3

How does simple harmonic motion apply to resonance?