AQA A-Level Physics Paper 1, November 2020: Question 25
1 mark · Medium difficulty · Multiple Choice
Calculate the frequency of vertical oscillations for a mass suspended from a light spring of known stiffness.
Practise this questionQuestion
Question text
25 A mass of 0.90 kg is suspended from the lower end of a light spring of stiffness 80 N m−1.
When the mass is displaced vertically and released, it undergoes vertical oscillations of
small amplitude.
What is the frequency of the oscillations?
[1 mark]
A 0.071 Hz
B 0.67 Hz
C 1.50 Hz
D 14 Hz
Mark scheme
Show the mark scheme
25 C
How to answer it
Frequency of a Mass-Spring System
What this question tests
This question assesses your ability to recall and apply the equation for the frequency of a mass-spring oscillating system undergoing Simple Harmonic Motion (SHM). It tests unit conversion awareness, formula manipulation (linking mass, spring constant, period, and frequency), and handling significant figures in multiple-choice calculations.
Exam Question Breakdown
Part 25 — Calculating Frequency
✅ Correct Answer
C (1.50 Hz)
💡 Key Knowledge
- The period T of a mass-spring system is given by: T = 2 π √(m / k)
- Frequency f is the reciprocal of period: f = 1 / T
- Combining these gives the frequency formula: f = (1 / (2 π)) √(k / m)
- Always ensure mass is in standard SI units ( kg ) and spring constant is in N m⁻¹ .
🧠 Exam Technique
- Check your calculator mode: Ensure you are not in gradient or radian mode unnecessarily when using trigonometric functions elsewhere, though standard constants apply here.
- Don't stop halfway: A very common multiple-choice trap is calculating the period T and accidentally picking the option that matches that value instead of inverting it to find f .
❌ Common Errors
- Inverting the ratio: Accidentally using √(m / k) inside the frequency equation instead of √(k / m) .
- Forgetting 2 π: Omitting the 2 π factor, which stems from treating SHM as uniform circular motion projections.
- Stopping at Period: Calculating T ≈ 0.67 s (Option B) and selecting it without realizing the question asked for frequency.
📐 Step-by-Step Calculation
- Identify given variables: Mass m = 0.90 kg , Spring constant k = 80 N m⁻¹ .
- State the frequency formula for a mass-spring system:
f = (1 / (2 π)) √(k / m) - Substitute the values into the equation:
f = (1 / (2 × π)) √(80 / 0.90) - Evaluate the term inside the square root:
√(88.889) ≈ 9.428 - Complete the calculation and apply sig figs:
f = 9.428 / (2 × π) = 1.5002... Hz
Rounding to 3 significant figures (matching the precision of the input data) gives 1.50 Hz.
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.