Physics 9702 · syllabus 17
Cambridge A Level Physics 9702 — Oscillations topical past papers
Simple harmonic motion and its equations, the exchange between kinetic and potential energy, damping, forced oscillations and resonance.
- Questions
- 103
- Years
- 2009–2026
- With mark scheme
- 100%
- Questions 2022–2026
- 28
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What Oscillations covers
Simple harmonic motion happens whenever an object's acceleration is proportional to its displacement from a fixed point and directed back towards that point: a = −ω²x. A mass on a spring and a pendulum swinging through small angles both fit this description. The solution x = x₀ sin ωt describes the displacement, with ω = 2πf, and the velocity follows as v = v₀ cos ωt, reaching its maximum ωx₀ at the centre and zero at the extremes.
Displacement, velocity and acceleration all vary sinusoidally: velocity is a quarter-cycle out of step with displacement, and acceleration is in antiphase with it. Energy passes back and forth between kinetic and potential stores while the total, ½mω²x₀², stays constant in an undamped system, and you should be able to read any of these quantities from a graph of another.
Real oscillators lose energy to resistive forces. Light damping lets the amplitude decay gradually; critical damping returns the system to equilibrium in the shortest time without overshooting; heavy damping returns it slowly. Driving a system at its natural frequency produces the largest amplitude, which is resonance. This is A Level content, examined on Paper 4; it builds on circular motion, and the same sinusoidal mathematics returns in alternating currents.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- 17 Oscillations
- 17.1 Simple harmonic oscillations
- 17.2 Energy in simple harmonic motion
- 17.3 Damped and forced oscillations, resonance
What you should be able to do
- Show that a system moves with simple harmonic motion by identifying a ∝ −x
- Use x = x₀ sin ωt, v = v₀ cos ωt and v = ±ω√(x₀² − x²)
- Interpret and sketch graphs of displacement, velocity, acceleration and energy against time or displacement
- Calculate the total energy ½mω²x₀² and describe how it is shared between kinetic and potential energy
- Sketch displacement–time graphs for light, critical and heavy damping
- Explain resonance as the maximum amplitude reached when the driving frequency equals the natural frequency
Key ideas
- Defining equation a = −ω²x, with ω = 2πf = 2π/T (rad s⁻¹)
- x = x₀ sin ωt and v = v₀ cos ωt, with v₀ = ωx₀
- v = ±ω√(x₀² − x²); the maximum acceleration, ω²x₀, occurs at the extremes
- Total energy E = ½mω²x₀²; kinetic energy at displacement x is ½mω²(x₀² − x²)
How Oscillations has been examined
From 2022 to 2026, Oscillations was on Paper 4 · A Level Structured Questions in 11 of 11 exam series, worth about 8% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 4 · A Level Structured Questions | 28 | 8% | 11 of 11 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 9.
Filed in Momentum under: Oscillations.
A worked example
A 0.30 kg mass on a spring oscillates with simple harmonic motion of amplitude 4.0 cm and frequency 2.5 Hz. Find its speed when it is 2.0 cm from the equilibrium position, and the total energy of the oscillation.
- ω = 2πf = 2π × 2.5 = 15.7 rad s⁻¹
- v = ω√(x₀² − x²) = 15.7 × √(0.040² − 0.020²) = 15.7 × 0.0346 = 0.544 m s⁻¹
- E = ½mω²x₀² = ½ × 0.30 × 15.7² × 0.040² = 0.059 J
- Check: the kinetic energy at 2.0 cm is ½ × 0.30 × 0.544² = 0.044 J, three quarters of the total, as ½mω²(x₀² − x²) predicts
Answer: Speed 0.54 m s⁻¹; total energy 5.9 × 10⁻² J
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Using f where ω belongs — ω = 2πf, so leaving out the 2π makes speeds wrong by a factor of 6.3 and accelerations by a factor of 39
- Saying the acceleration is greatest at the centre because the speed is — acceleration is greatest at the extremes, where the displacement is largest, and zero at the centre
- Evaluating sin ωt with the calculator in degree mode — ωt is in radians
- Describing critical damping as the oscillation dying away quickly — the system does not oscillate at all; it returns to equilibrium in the shortest possible time
- Saying resonance happens when the driving frequency is high — it happens when the driving frequency equals the natural frequency
Exam technique
- When asked to show that a motion is simple harmonic, give both parts: acceleration proportional to displacement, and directed opposite to it, towards the equilibrium position
- Match the equation to the starting point: x = x₀ sin ωt starts at the centre, so if timing starts at an extreme, use x = x₀ cos ωt
- On energy–displacement graphs, draw kinetic energy as an inverted parabola and potential energy as an upright one, with their sum a horizontal line
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.