# Explain how the kinetic energy and potential energy of an object undergoing simple harmonic motion vary with time over one complete oscillation, and identify the time within one cycle at which the rate of energy transfer between kinetic and potential energy is greatest.

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

> An object oscillates with simple harmonic motion about its equilibrium position with period T.

## Mark scheme (4 marks)

1. Kinetic energy is maximum at the equilibrium position (zero displacement) and minimum (zero) at maximum displacement (amplitude).
2. Potential energy is maximum at maximum displacement (amplitude) and minimum (zero) at the equilibrium position, so it varies in the opposite sense to kinetic energy.
3. Both kinetic and potential energy vary periodically with a period of T/2 (i.e. they each complete two full cycles per oscillation), since both are proportional to the square of a sinusoidal function.
4. The rate of energy transfer between KE and PE is greatest when the object is at the equilibrium position (or equivalently at T/4, 3T/4, etc. after release from rest at amplitude), because this is where the gradient of each energy–time graph is steepest / the speed is changing most rapidly.

## Key terms

- [simple harmonic motion](https://www.gradenine.co.uk/glossary/simple-harmonic-motion)
- [kinetic energy](https://www.gradenine.co.uk/glossary/kinetic-energy)
- [potential energy](https://www.gradenine.co.uk/glossary/potential-energy)
- [rate of energy transfer](https://www.gradenine.co.uk/glossary/rate-of-energy-transfer)

## 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-kinetic-energy-and-2154dff8) · Published by Druglandscape Ltd.