# Explain how the restoring force acting on a mass–spring system gives rise to simple harmonic motion, and state the condition on this force that must be satisfied for the motion to be classified as simple harmonic.

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

> A block of mass m is attached to a horizontal spring of spring constant k and rests on a frictionless surface. The block is displaced from its equilibrium position and released.

## Mark scheme (4 marks)

1. When displaced, the spring exerts a restoring force directed towards the equilibrium position (opposing the displacement).
2. The magnitude of the restoring force is proportional to the displacement from equilibrium (F = −kx), so the acceleration is also proportional to displacement.
3. Because the net force (and hence acceleration) is always directed towards equilibrium, the block overshoots, creating an oscillatory motion about the equilibrium position.
4. The condition for SHM is that the acceleration (or restoring force) must be directly proportional to displacement and directed towards the equilibrium position / opposite to the displacement.

## Key terms

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

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-how-the-restoring-force-acting-0654a7f8) · Published by Druglandscape Ltd.