A guitar string is plucked and vibrates in simple harmonic motion. Explain how the displacement, velocity, and acceleration of the string change as it moves from its maximum displacement back to its equilibrium (undisturbed) position, and state what happens to the amplitude of the vibrations over time if no further energy is supplied.

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

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

When a guitar string is plucked, it is displaced from its equilibrium position and then released, oscillating back and forth in simple harmonic motion.

Model answer (5 marks)

At the maximum displacement the string is momentarily at rest, so its velocity is zero. As it moves towards the equilibrium position the restoring force increases, causing the velocity to increase. The acceleration, which is proportional to the restoring force, is greatest at the maximum displacement and directed towards the equilibrium position. When the string passes through the equilibrium position the restoring force is zero, so the velocity is at its maximum. If no further energy is supplied the amplitude of the vibrations gradually decreases as energy is lost to the surroundings, so the oscillations die away over time.

Examiner tips

  • Mention zero velocity at extreme, increasing velocity towards centre, maximum velocity at centre, greatest acceleration at extremes, and amplitude decay due to damping.
  • Use the correct terminology: displacement, velocity, acceleration, restoring force, amplitude, damping.
  • Keep the answer concise – 5 points, no extra words.

Common mistakes

  • Saying the velocity is maximum at the extremes instead of at the equilibrium position.
  • Forgetting that acceleration is greatest at the extremes, not at the centre.
  • Claiming the amplitude increases over time without energy input.

Mark scheme (5 marks)

  1. At maximum displacement the velocity of the string is zero
  2. As the string moves towards the equilibrium position, its velocity increases
  3. The acceleration (restoring force) is greatest at maximum displacement and directed towards the equilibrium position
  4. At the equilibrium position, velocity is at its maximum
  5. Without an energy input, the amplitude decreases over time (the vibrations die away / the string loses energy to its surroundings)

Key terms in this question

amplitude · displacement · simple harmonic motion · acceleration

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