# Simple harmonic motion

Back-and-forth motion where the restoring force is proportional to the displacement and points back to the middle.

Physics (university) · Part 05: Oscillations and waves · Card 1 of 11 · Last updated 2026-10-19

## Analogy

A child on a swing that keeps returning to the lowest point.

## Example

**Position over time**

x = A cos(omega t)
A = 0.10 m, omega = 6.28 rad/s
At t = 0, x = 0.10 m

## In practice

A mass on a spring swings between +A and -A, so the largest displacement is the amplitude.

## Questions people ask

### What makes motion simple harmonic?

The restoring force must be proportional to displacement and point back toward the centre, like F = -kx. This makes the motion a smooth sine wave. A spring with small stretches and a pendulum with small angles are the standard examples, but big angles break the rule.

### Where is the speed greatest in SHM?

The speed is greatest at the centre, where the mass passes through the equilibrium point. There all the energy is kinetic. At the ends of the swing the mass stops for an instant, and all the energy is stored as potential energy in the spring.

## Related concepts

- [Period and frequency](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-2)
- [Mass on a spring](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-3)
- [Simple pendulum](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-4)
- [Resonance](https://studyvisually.com/learn/science/physics-university/physics-university-part-5/physics-university-part-5-concept-5)

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