Explain how the acceleration of an object undergoing simple harmonic motion varies with displacement from the equilibrium position, and state what this tells us about the direction of the net force acting on the object.

IB DP Physics Standard Level (2023 syllabus) — C.1 Simple harmonic motion · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

A mass attached to a horizontal spring oscillates on a frictionless surface. The mass is displaced from its equilibrium position and released.

Model answer (4 marks)

The acceleration is directly proportional to the displacement from the equilibrium position.
The acceleration is always directed towards the equilibrium position (i.e. opposite in direction to the displacement).
Therefore the net (restoring) force is always directed towards the equilibrium position.
At maximum displacement (the amplitude) the acceleration / net force is greatest, and at the equilibrium position the acceleration / net force is zero.

Examiner tips

  • Use the proportionality a∝x to justify the relationship; mention Hooke’s law. State clearly that the direction is opposite to the displacement. Highlight that the force is restoring. Include the extremes (maximum at amplitude, zero at equilibrium).

Common mistakes

  • Confusing acceleration with velocity or force. Saying the force is always in the same direction as the displacement. Omitting the proportionality statement or the zero acceleration at equilibrium.

Mark scheme (4 marks)

  1. The acceleration is directly proportional to the displacement from the equilibrium position.
  2. The acceleration is always directed towards the equilibrium position (i.e. opposite in direction to the displacement).
  3. Therefore the net (restoring) force is always directed towards the equilibrium position.
  4. At maximum displacement (amplitude) the acceleration / net force is greatest, and at the equilibrium position the acceleration / net force is zero.

Key terms in this question

simple harmonic motion · equilibrium position · displacement · acceleration

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