Simple harmonic oscillations
Cambridge A-Level Physics (9702) · Unit 17: Oscillations · 9 flashcards
Simple harmonic oscillations is topic 17.1 in the Cambridge A-Level Physics (9702) syllabus , positioned in Unit 17 — Oscillations , alongside Energy in simple harmonic motion and Damped and forced oscillations, resonance. In one line: Displacement (x): distance from equilibrium. Amplitude (x₀): max displacement. Period (T): time for one complete oscillation. Frequency (f): number of oscillations per unit time. f = 1/T.
Marked as A2 Level: examined at A Level in Paper 4 (A Level Structured Questions) and Paper 5 (Planning, Analysis and Evaluation). It is not tested on the AS-only papers (Papers 1, 2 and 3).
The deck below contains 9 flashcards — 2 definitions, 5 key concepts and 2 calculations — covering the precise wording mark schemes reward. Use the 2 definition cards to lock down command-word answers (define, state), then move on to the concept and calculation cards to handle explain, describe, calculate and compare questions.
Displacement, amplitude, period, and frequency in the context of oscillations
Displacement (x): distance from equilibrium. Amplitude (x₀): max displacement. Period (T): time for one complete oscillation. Frequency (f): number of oscillations per unit time. f = 1/T
What the Cambridge 9702 syllabus says
2025-2027 syllabus, in our words · A2 LevelWhat the syllabus expects you to be able to do in this topic, in plain English. For the exact wording, see the official syllabus (PDF).
- Understand and use, for oscillations, the terms amplitude, displacement, frequency, angular frequency, period and phase difference, and write the period in terms of frequency (T = 1/f) and of angular frequency (T = 2π/ω).
- Understand that motion is simple harmonic when, relative to a fixed point, the acceleration is opposite in direction to the displacement and proportional to it.
- Recall and use x = x₀ sin ωt as a solution of a = −ω²x, and use the equation a = −ω²x itself.
- Use v = ±ω√(x₀² − x²) and v = v₀ cos ωt for the velocity in simple harmonic motion.
- Analyse and interpret graphs showing how displacement, velocity and acceleration vary in simple harmonic motion.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 9702 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Tips to avoid common mistakes in Simple harmonic oscillations
- › Explicitly state that the minus sign shows acceleration is always in the opposite direction to displacement and directed towards the equilibrium position.
Define displacement, amplitude, period, and frequency in the context of oscillations.
Displacement (x): distance from equilibrium. Amplitude (x₀): max displacement. Period (T): time for one complete oscillation. Frequency (f): number of oscillations per unit time. f = 1/T
Define angular frequency (ω) and how it relates to period (T) and frequency (f).
Angular frequency (ω) is the rate of change of angular displacement, measured in rad/s. ω = 2πf and ω = 2π/T. It's useful in describing circular motion and oscillations.
State the condition for Simple Harmonic Motion (SHM).
Simple Harmonic Motion occurs when the acceleration (a) of an object is proportional to its displacement (x) from a fixed point and in the opposite direction. Mathematically: a = -ω²x.
What is the significance of the negative sign in the equation a = -ω²x for SHM?
The negative sign indicates that the acceleration is always directed towards the equilibrium position, opposite to the displacement. This restoring force is what drives the oscillation.
Given a = –ω²x, state a solution for the displacement (x) as a function of time (t).
A solution to the equation a = –ω²x is x = x₀ sin(ωt), where x₀ is the amplitude and ω is the angular frequency. This describes how the displacement varies sinusoidally with time.
Write down the equation for velocity (v) as a function of time (t) in SHM.
The velocity (v) as a function of time (t) is given by v = v₀ cos(ωt), where v₀ is the maximum velocity (amplitude of velocity).
Write down the equation for velocity (v) as a function of displacement (x) in SHM.
The velocity (v) as a function of displacement (x) is given by v = ± ω√(x₀² - x²), where x₀ is the amplitude and ω is the angular frequency.
Describe the phase relationship between displacement, velocity, and acceleration in SHM.
In SHM, velocity leads displacement by π/2 (90°), and acceleration leads velocity by π/2 (90°). Therefore, acceleration and displacement are π (180°) out of phase.
Sketch graphs of displacement, velocity, and acceleration against time for SHM, highlighting key relationships.
Displacement (x) is a sine/cosine curve. Velocity (v) is the derivative of displacement (a cosine/sine curve, 90° ahead). Acceleration (a) is the derivative of velocity (negative sine/cosine, 180° out of phase with displacement). Note the max/min points.
Review the material
Read full revision notes on Simple harmonic oscillations — definitions, equations, common mistakes, and exam tips.
Read NotesMore topics in Unit 17 — Oscillations
Simple harmonic oscillations sits alongside these A-Level Physics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Key terms covered in this Simple harmonic oscillations deck
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