A mass is attached to a spring and set into simple harmonic motion by pulling the mass downward from its equilibrium position and releasing it. Describe the motion of the mass during one complete oscillation, referring to displacement, amplitude, and how the restoring force affects the motion.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A mass-spring system oscillates vertically. The mass is released from a maximum displacement of 4 cm below the equilibrium position.
Model answer (5 marks)
1. The mass starts at its maximum displacement of 4 cm below the equilibrium position – this is the amplitude.
2. A restoring force from the spring acts upward, towards the equilibrium, causing the mass to accelerate back towards equilibrium.
3. The mass passes through the equilibrium position (zero displacement) where its speed is greatest.
4. It continues past equilibrium, reaching a maximum displacement of 4 cm above equilibrium – the same amplitude on the opposite side.
5. The mass then returns to the starting point, completing one full oscillation in one period.
2. A restoring force from the spring acts upward, towards the equilibrium, causing the mass to accelerate back towards equilibrium.
3. The mass passes through the equilibrium position (zero displacement) where its speed is greatest.
4. It continues past equilibrium, reaching a maximum displacement of 4 cm above equilibrium – the same amplitude on the opposite side.
5. The mass then returns to the starting point, completing one full oscillation in one period.
Examiner tips
- Use the word "amplitude" for the maximum displacement; include the 4 cm figure. Mention the restoring force direction and its effect on acceleration. State that speed is greatest at equilibrium. Show the symmetry of the motion. Finish with the period completing the cycle.
Common mistakes
- Confusing the direction of the restoring force (upward vs downward). Forgetting to mention that speed is greatest at equilibrium. Not recognising that the amplitude is the same on both sides of equilibrium.
Mark scheme (5 marks)
- The mass starts at maximum displacement (amplitude) below the equilibrium position
- A restoring force acts towards the equilibrium position, causing the mass to accelerate back towards equilibrium
- The mass passes through the equilibrium position (zero displacement) where its speed is greatest
- The mass overshoots equilibrium and reaches maximum displacement on the opposite side (above equilibrium), equal to the original amplitude
- The mass returns to its original starting position, completing one full oscillation in a time equal to the time period
Key terms in this question
amplitude · displacement · equilibrium position · restoring force
Related
- All Eduqas A-Level Physics revision notes →
- How to answer a "Describe" question →
- Decode the mark scheme abbreviations →
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