Explain how the restoring force acting on an object undergoing simple harmonic motion (SHM) gives rise to the periodic nature of the motion.

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 small object is attached to a horizontal spring on a frictionless surface and displaced from its equilibrium position before being released.

Model answer (4 marks)

The restoring force is always directed towards the equilibrium position, i.e. it is opposite to the displacement. Its magnitude is proportional to the displacement (F=−kx), so the acceleration is also proportional to the displacement. When the object is released it accelerates towards equilibrium, but because it has inertia it overshoots the equilibrium position. At this point the displacement has changed sign, so the restoring force now acts in the opposite direction. The object then accelerates back, again overshoots, and the process repeats. This continuous reversal of direction and acceleration produces a periodic, oscillatory motion about the equilibrium position.

Examiner tips

  • Use the phrase ‘directed towards the equilibrium position’ to show direction of force.
  • Mention the proportionality F=−kx to link force and displacement.
  • Explain the overshoot due to inertia to show why the motion is periodic.
  • Keep the answer concise – 4 points only.

Mark scheme (4 marks)

  1. The restoring force is always directed towards the equilibrium position (opposite to the displacement).
  2. The magnitude of the restoring force (and therefore the acceleration) is proportional to the displacement from equilibrium.
  3. The object accelerates towards equilibrium, overshoots (due to its inertia / velocity at equilibrium), and the restoring force then acts in the opposite direction again.
  4. This process repeats continuously, producing periodic (oscillatory) motion about the equilibrium position.

Key terms in this question

restoring force · simple harmonic motion (SHM)

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