# Explain why the total mechanical energy of an object undergoing simple harmonic motion remains constant, and describe how the kinetic and potential energies vary with displacement from the equilibrium position.

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

> An object of mass m oscillates in simple harmonic motion with amplitude A and angular frequency ω.

## Mark scheme (4 marks)

1. No dissipative (resistive/frictional) forces act in ideal SHM, so no energy is lost to the surroundings, meaning total mechanical energy is conserved.
2. Kinetic energy is maximum at the equilibrium position (zero displacement) and zero at maximum displacement (amplitude).
3. Potential energy is maximum at maximum displacement (amplitude) and zero at the equilibrium position.
4. At any displacement, kinetic and potential energies are complementary — as one increases the other decreases by the same amount — so their sum (total mechanical energy = ½mω²A²) remains constant.

## Key terms

- [simple harmonic motion](https://www.gradenine.co.uk/glossary/simple-harmonic-motion)
- [equilibrium position](https://www.gradenine.co.uk/glossary/equilibrium-position)
- [total mechanical energy](https://www.gradenine.co.uk/glossary/total-mechanical-energy)

## 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-why-the-total-mechanical-energy-41888a0c) · Published by Druglandscape Ltd.