AQA A-Level Physics Paper 1, November 2020: Question 24

1 mark · Medium difficulty · Multiple Choice

Determine the total energy of a particle of mass m undergoing simple harmonic motion with amplitude A and frequency f.

Practise this question

Question

Multiple choice question 24 asking for the total energy of a particle of mass m undergoing simple harmonic motion with amplitude A and frequency f. Four options are provided: A (2 pi mf A^2), B (2 pi^2 m f^2 A^2), C (4 pi^2 m^2 f^2 A), and D (4 pi^2 m f^2 A^2).
Question text

24 A particle of mass m undergoes simple harmonic motion with amplitude A and frequency f.

What is the total energy of the particle?

[1 mark]

A 2πmfA2

B 2π2mf 2A2

C 4π2m2f 2A

D 4π2mf 2A2

Mark scheme

Show the mark scheme Mark scheme indicating the correct answer is B.

24 B

How to answer it

Total Energy in Simple Harmonic Motion (SHM)

What this question tests

This question tests your recall and derivation skills regarding energy conservation in Simple Harmonic Motion (SHM). Specifically, it assesses your ability to combine the maximum kinetic energy formula with standard angular frequency substitutions (omega = 2 pi f) to express total energy in terms of mass (m), frequency (f), and amplitude (A).

Question Part 2.4 [1 mark]

Multiple Choice Solution

✅ Correct Answer: B

The correct option is B ( 2π²mf²A² ).

Awarded 1 mark for selecting B.

💡 Key Knowledge

  • Total energy (E) in SHM equals the maximum kinetic energy: E = 0.5 m v_max²
  • Maximum velocity in SHM is given by: v_max = ω A
  • Angular frequency is linked to frequency by: ω = 2 π f

📐 Step-by-Step Derivation

  1. Start with the total energy expression: E = 0.5 m v_max²
  2. Substitute maximum velocity: E = 0.5 m (ω A)² = 0.5 m ω² A²
  3. Substitute angular frequency ( ω = 2 π f ): E = 0.5 m (2 π f)² A²
  4. Expand the bracket: E = 0.5 m (4 π² f²) A²
  5. Simplify coefficients: E = 2 π² m f² A²

❌ Common Errors & Traps

  • Option D trap ( 4π²mf²A² ): Forgetting to square the 2 when expanding (2πf)² , leading to an incorrect coefficient of 4 instead of 2.
  • Forgetting squared terms: Confusing maximum velocity ( ωA ) with displacement or failing to square the frequency and amplitude parameters.

🧠 Exam Technique & Examiner Insights

In multiple-choice questions involving algebraic derivations, do not guess. Quickly derive the formula on your rough paper using foundational equations (like maximum kinetic energy) to verify dimensional correctness and numerical coefficients before locking in your answer choice.

Topics

Physics · 3.6 Further mechanics and thermal physics (A-level only)

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, November 2020. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.