Topic 13: Oscillations — Edexcel A-Level Physics
Test yourself on Topic 13: Oscillations with PEARSON EDEXCEL A-Level practice questions.
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Topic 13: Oscillations explained
Simple harmonic motion (SHM) arises whenever the resultant force on a body is proportional to its displacement from an equilibrium position and directed back towards that position.
Read the full explanation
The defining condition is F = −kx: the minus sign shows the force opposes the displacement, and k is a positive constant (the force per unit displacement, in N m⁻¹). To identify SHM in a situation, define the equilibrium position, write the resultant force in terms of displacement x from it, and check that the force is proportional to x and oppositely directed. For a mass on a spring, the restoring force is proportional to extension, so SHM occurs for displacements within the elastic limit. For a pendulum, the component of weight along the arc is proportional to displacement only for small angles. If the force is constant, or proportional to x but in the same direction, the motion is not SHM.
Your focus
- State the condition for simple harmonic motion as F = −kx and explain the meaning of each term.
- Test a described physical situation against the condition to decide whether SHM occurs.
- Explain the limits within which a spring or pendulum approximates SHM.
Topic 13: Oscillations exam tips
Marking Points
- States the SHM condition as F = −kx, with the resultant (restoring) force proportional to displacement from equilibrium.
- Explains that the minus sign means the force acts in the opposite direction to the displacement, i.e. towards equilibrium.
- Identifies k as a positive constant equal to force per unit displacement, with units N m⁻¹.
- Recognises that SHM requires the resultant force, not any single applied force, to satisfy the condition.
- Applies the test to a context: e.g. a mass on a spring obeys F = −kx within the elastic limit, whereas a pendulum approximates SHM only for small angular displacements.
- Rejects situations where the force is constant or directed away from equilibrium as not SHM.
Examiner Tips
- 💡Always define the equilibrium position and the displacement x before testing the condition.
- 💡Check both features: proportionality to x and opposite direction; state both explicitly.
- 💡For real systems, note the limits (elastic limit for springs, small angles for pendulums) within which the condition holds.
Common Mistakes
- Treating the minus sign as merely a direction convention to be ignored: the correction is that the minus sign is essential, showing the force always opposes displacement.
- Assuming any oscillation is SHM: the correction is that SHM requires the resultant force to be proportional to displacement, which many oscillations (e.g. large-angle pendulum swings) do not satisfy.
- Using the applied force rather than the resultant force in F = −kx: the correction is that only the resultant (restoring) force determines whether SHM occurs.