AQA A-Level Physics: Simple Harmonic Motion (SHM) and Damping — mark scheme explained

The question

Mark scheme, decoded

How the examiner actually awards the marks on this topic.

Gradora's own decode of the marking approach — not the exam board's published mark scheme.

Model answer

A full-mark response to the question above, worked through step by step.

⏱Timing: Allocate approximately 5 minutes for a 4-mark question and 7-8 minutes for a 6-mark question to ensure you have enough time to show all necessary steps and provide clear explanations.

1. 1. Identify the given values: m = 0.5 kg , k = 20 N/m .0 marks
2. 2. Use the formula for the period of a mass-spring system: T = 2π√(m/k) .1 mark
3. 3. Substitute the values into the formula: T = 2π√(0.5/20) = 2π√(0.025) ≈ 2π × 0.158 ≈ 0.994 s2 marks
4. 4. Round the answer to an appropriate number of significant figures: T ≈ 0.99 s .1 mark

Final answer: T ≈ 0.99 s

✓Work through every step correctly and you earn all 4 marks.

Common mistakes

• Forgetting to use the small-angle approximation in the derivation of the period for a simple pendulum.

  Why it happens: Students often overlook the importance of the small-angle approximation, which simplifies the equations and allows for the derivation of the period formula.

  Fix: Always remember that the small-angle approximation ( sin(θ) ≈ θ ) is necessary for deriving the period of a simple pendulum. This approximation is valid only for small angles (typically less than 10°).

• Confusing the formulas for the periods of mass-spring systems and simple pendulums.

  Why it happens: Students may mix up the formulas due to their similar forms, leading to incorrect calculations.

  Fix: Memorize the specific formulas for each system: T = 2π√(m/k) for mass-spring systems and T = 2π√(l/g) for simple pendulums. Practice using these formulas in different contexts to reinforce their differences.

• Failing to recognize the conservation of total energy in SHM.

  Why it happens: Students might not fully understand that the total energy is constant and equal to the sum of kinetic and potential energies.

  Fix: Understand that in SHM, the total energy E total is conserved and given by E total = 0.5kA 2 . Practice problems involving the variation of kinetic and potential energies with displacement and time to reinforce this concept.

• Incorrectly identifying the points where kinetic and potential energies are maximum in SHM.

  Why it happens: Students may confuse the points where E k and E p are maximum, leading to incorrect energy graphs or calculations.

  Fix: Remember that kinetic energy is maximum at the equilibrium position (where displacement is zero) and potential energy is maximum at the maximum displacement. Practice drawing energy graphs and solving problems involving these points to solidify your understanding.

• Misunderstanding the effects of different types of damping on oscillations.

  Why it happens: Students may not fully grasp how light, critical, and heavy damping affect the amplitude and period of oscillations.

  Fix: Understand that light damping results in a slow decrease in amplitude with nearly constant period, critical damping returns the system to equilibrium as quickly as possible without oscillating, and heavy (over) damping returns the system to equilibrium slowly without oscillating, taking longer than critical damping. Practice problems involving damped oscillators to reinforce these concepts.

• Forgetting to use the correct units when calculating period or frequency.

  Why it happens: Students may overlook the importance of using consistent units, leading to incorrect answers.

  Fix: Always check that all values are in consistent units before substituting them into formulas. For example, ensure that mass is in kilograms, spring constant is in newtons per meter, and length is in meters. Practice unit conversions if necessary.

Where the marks go

The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.

Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.

Related questions

• AQA A-Level Physics: Fundamental and Derived Units in Physics — mark scheme explained →
• AQA A-Level Physics: Errors and Uncertainties in Measurements — mark scheme explained →