A mass is attached to a spring and set into simple harmonic motion by being pulled down and released. Describe the motion of the mass, including how displacement, velocity, and restoring force change during one complete oscillation.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A mass hanging on a vertical spring is pulled downwards from its equilibrium position and released. It then oscillates up and down in simple harmonic motion.
Model answer (5 marks)
The mass oscillates about the equilibrium (undisturbed) position.
At the start the mass is pulled down to a maximum displacement (the amplitude) and released.
• Displacement is greatest at the two extreme positions and is zero at the equilibrium position.
• The restoring force, which is proportional to the displacement (F = –kx), is always directed towards the equilibrium position and is greatest in magnitude at the maximum displacement.
• The velocity is zero at the maximum displacement and increases as the mass moves towards the equilibrium, reaching its greatest magnitude (maximum speed) at the equilibrium position. It then decreases again as the mass moves to the opposite extreme.
• After one complete oscillation the mass returns to its starting position with the same displacement, and the motion repeats with a fixed time period.
At the start the mass is pulled down to a maximum displacement (the amplitude) and released.
• Displacement is greatest at the two extreme positions and is zero at the equilibrium position.
• The restoring force, which is proportional to the displacement (F = –kx), is always directed towards the equilibrium position and is greatest in magnitude at the maximum displacement.
• The velocity is zero at the maximum displacement and increases as the mass moves towards the equilibrium, reaching its greatest magnitude (maximum speed) at the equilibrium position. It then decreases again as the mass moves to the opposite extreme.
• After one complete oscillation the mass returns to its starting position with the same displacement, and the motion repeats with a fixed time period.
Examiner tips
- Use the phrase ‘restoring force always acts towards the equilibrium position’ to gain the full point on the force. Use the word ‘maximum’ for both displacement and velocity at the correct points. Mention that the motion repeats with a fixed period to cover the final point.
Common mistakes
- Saying the restoring force is greatest at the equilibrium position (it is actually greatest at the amplitude). Forgetting that velocity is zero at the maximum displacement. Not stating that the motion repeats with a fixed period.
Mark scheme (5 marks)
- The mass oscillates about the equilibrium (undisturbed) position
- The restoring force always acts towards the equilibrium position / opposes displacement
- Restoring force (and acceleration) is greatest at maximum displacement / at the amplitude
- Velocity is zero at maximum displacement (amplitude) and greatest/maximum at the equilibrium position
- One complete oscillation returns the mass to its starting position with the same displacement / the motion repeats with a fixed time period
Key terms in this question
simple harmonic motion · displacement · restoring force
Related
- All WJEC A-Level Physics (Wales) revision notes →
- How to answer a "Describe" question →
- Decode the mark scheme abbreviations →
More Simple harmonic motion questions
- A pendulum swings back and forth in simple harmonic motion. Describe the energy …
- A buoy floating on the surface of the sea bobs up and down in simple harmonic mo…
- A guitar string is plucked and vibrates in simple harmonic motion. Explain how t…
- A child sits on a swing in a playground. The swing is pulled back and released, …