# Explain how the velocity and acceleration of an object undergoing simple harmonic motion (SHM) vary with displacement from the equilibrium position, and identify the displacement at which each quantity reaches its maximum magnitude.

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

## Mark scheme (4 marks)

1. Acceleration is directly proportional to displacement from equilibrium and directed towards the equilibrium position (restoring direction).
2. Acceleration reaches its maximum magnitude at maximum displacement (amplitude) from equilibrium.
3. Velocity is zero at maximum displacement and increases as the object moves towards the equilibrium position, because the restoring force does work on the object, converting potential energy to kinetic energy.
4. Velocity reaches its maximum magnitude at the equilibrium position (zero displacement), where acceleration is zero.

## Key terms

- [simple harmonic motion (SHM)](https://www.gradenine.co.uk/glossary/simple-harmonic-motion-shm)
- [equilibrium position](https://www.gradenine.co.uk/glossary/equilibrium-position)
- [displacement](https://www.gradenine.co.uk/glossary/displacement)
- [acceleration](https://www.gradenine.co.uk/glossary/acceleration)
- [velocity](https://www.gradenine.co.uk/glossary/velocity)

## 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-velocity-and-acceleration-f26526ad) · Published by Druglandscape Ltd.