A buoy floating on the surface of the sea bobs up and down in simple harmonic motion as waves pass beneath it. The buoy starts at its maximum displacement above the equilibrium position and is then released. Describe the motion of the buoy over one complete oscillation, including how its speed and displacement change throughout.

WJEC A-Level Physics (Wales) — 5.1 Simple harmonic motion · Describe · 5 marks · View as Markdown

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

A buoy is anchored in open water. Ocean waves cause it to oscillate vertically with a regular time period. At the start of the observation, the buoy is at its maximum displacement above its equilibrium (undisturbed) position.

Model answer (5 marks)

1. At the instant it is released it is at the maximum displacement (amplitude) above equilibrium and its speed is zero.
2. From this point it accelerates towards the equilibrium position because the restoring force is directed towards equilibrium.
3. As it passes the equilibrium position its speed reaches a maximum.
4. Continuing past equilibrium it decelerates, slowing down as it moves towards the maximum displacement below equilibrium.
5. When it reaches that point its speed is again zero; it then returns to the starting position, completing one full oscillation in a time equal to one period.

Examiner tips

  • Use the sequence: start at amplitude → accelerate → max speed at equilibrium → decelerate → return to amplitude. Mention zero velocity at both amplitudes and maximum speed at equilibrium. Show that the time taken is one period.

Common mistakes

  • Forgetting that velocity is zero at both maximum displacements. Confusing the direction of acceleration with the direction of motion. Not recognising that the whole cycle takes one period.

Mark scheme (5 marks)

  1. At maximum displacement (amplitude) the buoy has zero velocity / is momentarily stationary
  2. The buoy accelerates towards the equilibrium position / restoring force acts towards equilibrium
  3. The buoy reaches maximum speed as it passes through the equilibrium (undisturbed) position
  4. The buoy then decelerates / slows down as it moves towards the maximum displacement below equilibrium
  5. The buoy returns to its original position (completing one full oscillation) in a time equal to one time period

Key terms in this question

equilibrium position · displacement · simple harmonic motion

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