AQA AS Level Physics Paper 2, June 2022: Question 14

1 mark · Medium difficulty · Multiple Choice

Determine the amplitude and period of vertical oscillations for a mass hanging on a spring when pulled down and released.

Practise this question

Question

A multiple-choice question numbered 14 states that a mass M hangs in equilibrium from a vertical spring, is pulled down by 10 cm and released, returning to equilibrium for the first time 0.50 s after release. A table presents four rows of options A to D for amplitude in cm and period in s.
Question text

14 A mass M hangs in equilibrium from a vertical spring that obeys Hooke’s law.

M is pulled down by 10 cm and then released to oscillate about the equilibrium position.

M returns to the equilibrium position for the first time 0.50 s after release.

Which row gives the amplitude and the period of the oscillations?

[1 mark]

Amplitude / cm Period / s

A 10 1.0

B 10 2.0

C 20 2.0

D 20 1.0

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer is B, with an amplitude of 10 cm and a period of 2.0 s.

14 B (AO1) 10 2.0

How to answer it

Spring-Mass System Amplitude and Period

What this question tests

This question assesses your understanding of simple harmonic motion (SHM) kinematics, specifically the definitions of amplitude and period for a vertical mass-spring system, and your ability to map the time taken for a fraction of a full oscillation cycle.

Question 14 — Multiple Choice

Determining Amplitude and Period from Release

✅ Correct Answer: Row B

Amplitude: 10 cm

Period: 2.0 s

Mark: 1 / 1 (AO1)

💡 Key Knowledge

  • Amplitude ($A$): The maximum displacement from the equilibrium position. Since M is pulled down by 10 cm and released, the maximum displacement is 10 cm .
  • Time Fraction: Moving from maximum displacement to the equilibrium position for the first time represents exactly 1/4 of a full oscillation cycle ( T/4 ).

🧠 Exam Technique

Do not rush multiple-choice questions involving SHM cycles. Sketch a quick displacement-time graph in your mind or on your exam paper starting at maximum displacement to clearly visualize that reaching the centre takes a quarter-period, not a half-period.

❌ Common Errors

  • Doubling the amplitude: Mistaking the total peak-to-peak distance ( 20 cm ) for the amplitude, which leads students to wrongly select rows C or D.
  • Miscalculating the period: Multiplying the time ( 0.50 s ) by 2 (assuming it represents half a cycle) instead of multiplying by 4 .

📐 Step-by-Step Working Out

  1. Identify Amplitude: The maximum displacement given in the stem is 10 cm . Amplitude is defined as maximum displacement, so A = 10 cm . This immediately narrows the choices to rows A and B.
  2. Relate Time to Period: The mass is released from maximum displacement and returns to equilibrium for the first time. This is one-quarter of a wave cycle. Therefore, T / 4 = 0.50 s .
  3. Calculate Period ($T$): Multiply the quarter-cycle time by 4: T = 0.50 s × 4 = 2.0 s .
  4. Match with Options: Amplitude = 10 cm and Period = 2.0 s points directly to Row B.

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.