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.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
Acceleration is directly proportional to displacement from equilibrium and directed towards the equilibrium position (restoring direction). It reaches its maximum magnitude at the maximum displacement (the amplitude) from equilibrium. 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. Velocity reaches its maximum magnitude at the equilibrium position (zero displacement), where acceleration is zero.
Examiner tips
- Use the proportionality a∝−x and state the direction; mention a=−ω²x.
- State that v=0 at x=±A and vmax at x=0; link to energy conversion.
Common mistakes
- Confusing the points of maximum velocity and acceleration; writing that both are at the amplitude.
- Omitting the restoring direction of the acceleration or the zero‑velocity at maximum displacement.
Mark scheme (4 marks)
- Acceleration is directly proportional to displacement from equilibrium and directed towards the equilibrium position (restoring direction).
- Acceleration reaches its maximum magnitude at maximum displacement (amplitude) from equilibrium.
- 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.
- Velocity reaches its maximum magnitude at the equilibrium position (zero displacement), where acceleration is zero.
Key terms in this question
simple harmonic motion (SHM) · equilibrium position · displacement · acceleration · velocity
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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