# Explain why the motion of a simple pendulum released from a small angle can be modelled as simple harmonic motion, and identify one condition under which this model would no longer be valid.

> IB DP Physics Standard Level (2023 syllabus) — C.1 Simple harmonic motion · Explain · 4 marks

> A simple pendulum consists of a small bob suspended from a fixed point by a light, inextensible string. When displaced from its equilibrium position and released, the bob oscillates back and forth.

## Mark scheme (4 marks)

1. The restoring force (or acceleration) is directed towards the equilibrium position
2. For small angles, the restoring force (or acceleration) is proportional to the displacement from equilibrium
3. These two conditions (restoring force directed towards equilibrium and proportional to displacement) satisfy the definition of simple harmonic motion
4. The model is no longer valid when the angle of displacement is large (greater than approximately 10°–15°), because the small-angle approximation breaks down and the restoring force is no longer proportional to displacement

## Key terms

- [simple harmonic motion](https://www.gradenine.co.uk/glossary/simple-harmonic-motion)

## Related

- [Revision notes for IB DP Physics Standard Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
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