A buoy floating on the sea bobs up and down in simple harmonic motion. Explain what is meant by simple harmonic motion and describe the resultant force and acceleration acting on the buoy at different positions during one complete oscillation.

AQA A-Level Physics (7408) — 3.6.1 Periodic Motion · Explain · 5 marks · View as Markdown

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

A buoy is anchored to the seabed. Ocean waves cause the buoy to oscillate vertically about its equilibrium position.

Model answer (5 marks)

Simple harmonic motion (SHM) is a type of periodic motion in which the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. For a buoy oscillating vertically, the buoy experiences a restoring force that pulls it back towards its equilibrium position.

Resultant force and acceleration:
1. At any displacement x from equilibrium, the resultant force F = –kx (k is a constant) and the acceleration a = –(k/m)x, so both are directed towards equilibrium.
2. At the equilibrium position (x = 0) the force and acceleration are zero.
3. At the maximum displacement (±A, the amplitude) the force and acceleration reach their maximum magnitudes, directed back towards equilibrium.
4. As the buoy moves from the maximum displacement towards equilibrium, the force and acceleration decrease in magnitude; when it passes equilibrium and continues to the opposite maximum, they increase in magnitude but reverse direction.

Examiner tips

  • Use the definition of SHM (force ∝ –displacement) to justify the direction of the force.
  • Show the force and acceleration are zero at equilibrium and maximum at amplitude.
  • Explain the change in magnitude as the buoy moves between these points.
  • Use correct symbols (F = –kx, a = –(k/m)x) to demonstrate proportionality.

Common mistakes

  • Confusing the direction of the force with the direction of motion; the force always points towards equilibrium.
  • Forgetting that acceleration is zero at equilibrium and maximal at amplitude.
  • Using the wrong proportionality sign (e.g., +kx instead of –kx).

Mark scheme (5 marks)

  1. The resultant force (and acceleration) always acts towards the equilibrium position
  2. The magnitude of the resultant force (and acceleration) is proportional to the displacement from the equilibrium position
  3. At the equilibrium position the resultant force is zero and the acceleration is zero
  4. At maximum displacement (amplitude) the resultant force and acceleration are at their maximum values
  5. As the buoy moves from maximum displacement back to equilibrium, the force and acceleration decrease; as it moves from equilibrium to the opposite maximum, the force and acceleration increase in the opposite direction

Key terms in this question

simple harmonic motion

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