A guitar string is plucked and vibrates in simple harmonic motion. Explain what is meant by simple harmonic motion and describe how the acceleration and displacement of the vibrating string are related throughout one complete oscillation.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
When a guitar string is plucked, it vibrates back and forth about its equilibrium position. The vibration gradually dies away as energy is transferred to the surroundings.
Model answer (5 marks)
Simple harmonic motion is a type of oscillation in which a body vibrates about an equilibrium position.
1. The motion is governed by a restoring force that is always directed towards the equilibrium position.
2. The restoring force is proportional to the displacement from equilibrium, so the acceleration a = –k x (or a = –ω²x).
3. Therefore the acceleration is always opposite in direction to the displacement.
4. When the string passes the equilibrium position the displacement is zero and the acceleration is zero.
5. At the extreme positions the displacement is maximum and the acceleration is at its maximum magnitude, directed back towards equilibrium.
1. The motion is governed by a restoring force that is always directed towards the equilibrium position.
2. The restoring force is proportional to the displacement from equilibrium, so the acceleration a = –k x (or a = –ω²x).
3. Therefore the acceleration is always opposite in direction to the displacement.
4. When the string passes the equilibrium position the displacement is zero and the acceleration is zero.
5. At the extreme positions the displacement is maximum and the acceleration is at its maximum magnitude, directed back towards equilibrium.
Examiner tips
- Use the phrase ‘restoring force proportional to displacement’ to hit the key point.
- Show the relationship a = –ω²x to demonstrate proportionality and direction.
- Mention zero displacement/acceleration at equilibrium and maximum values at extremes.
Common mistakes
- Confusing acceleration with velocity or force magnitude.
- Forgetting that acceleration is opposite in direction to displacement.
- Not recognising that acceleration is zero at the equilibrium position.
Mark scheme (5 marks)
- Simple harmonic motion involves oscillation/vibration about an equilibrium position
- There is a restoring force that always acts towards the equilibrium position
- Acceleration is proportional to displacement (from equilibrium)
- Acceleration is directed towards the equilibrium position / in the opposite direction to displacement
- At the equilibrium position, displacement is zero so acceleration is zero / at maximum displacement, acceleration is maximum
Key terms in this question
simple harmonic motion · displacement · acceleration
Related
- All Eduqas A-Level Physics revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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