AQA A-Level Physics Paper 1, June 2024: Question 30

1 mark · Medium difficulty · Multiple Choice

Calculate the speed of a body undergoing simple harmonic motion with an amplitude of 0.60 m and a period of 2 pi seconds when its displacement is 0.20 m.

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Question

Multiple choice question 30 asks for the speed of a body in simple harmonic motion with amplitude 0.60 m and period 2 pi seconds when its displacement is 0.20 m. Four options are given: A, 0.32 m s^-1; B, 0.57 m s^-1; C, 0.63 m s^-1; D, 22 m s^-1.
Question text

30 A body is in simple harmonic motion of amplitude 0.60 m and period 2π seconds.

What is its speed when its displacement is 0.20 m?

[1 mark]

A 0.32 m s−1

B 0.57 m s−1

C 0.63 m s−1

D 22 m s−1

Mark scheme

Show the mark scheme Mark scheme for question 30 showing the correct answer as option B, with a speed of 0.57 m s^-1.

30 B 0.57 m s−1 AO1

How to answer it

Calculating Speed in Simple Harmonic Motion (SHM)

What this question tests

This question assesses your ability to recall and apply the relationship between velocity, displacement, amplitude, and angular frequency in simple harmonic motion ( v = ±ω√(A² - x²) ), as well as calculating angular frequency ( ω = 2π / T ) from the given time period.

Question 30 • Multiple Choice • 1 Mark

Part 30: Determining Velocity at a Given Displacement

✅ Correct Answer: B

Option B: 0.57 m s⁻¹

Mark Awarded: 1 / 1 (AO1 - Demonstration of knowledge and application)

💡 Key Knowledge

  • Angular frequency definition: ω = 2π / T
  • SHM velocity equation: v = ±ω√(A² - x²)
  • Variables given: Amplitude A = 0.60 m , Period T = 2π s , Displacement x = 0.20 m .

🧠 Exam Technique

Look out for values given in terms of π (such as period T = 2π ). Do not convert π to a decimal prematurely; keeping it in algebraic form often simplifies calculations instantly before plugging numbers into your calculator.

❌ Common Errors

  • Calculator Mode Error: Accidentally leaving your calculator in degree mode instead of radian mode when evaluating trigonometric functions or angular parameters.
  • Mixing up A and x: Subtracting displacement squared from amplitude squared incorrectly inside the square root.

📐 Step-by-Step Calculation

  1. Step 1: Calculate the angular frequency ( ω )
    Using ω = 2π / T and given T = 2π s :
    ω = 2π / (2π) = 1 rad s⁻¹
  2. Step 2: Substitute values into the SHM velocity equation
    v = ω√(A² - x²)
    v = 1 × √(0.60² - 0.20²)
  3. Step 3: Evaluate inside the square root
    0.60² = 0.36
    0.20² = 0.04
    0.36 - 0.04 = 0.32
  4. Step 4: Complete the square root and final calculation
    v = 1 × √(0.32) ≈ 0.5657 m s⁻¹
    Rounding to 2 significant figures (matching the precision of the data given in the question): 0.57 m s⁻¹ (Option B).

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, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.