Where can I learn Simple harmonic oscillations for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 17.1 (Simple harmonic oscillations) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/17-1-simple-harmonic-oscillations.

Is Simple harmonic oscillations (17.1) on 9702 free to study?

Yes. The Physics 9702 course on MarkScheme is 100% free — including premium visual lessons, exam tips, and past-paper marking. No paywall for Simple harmonic oscillations.

How do I revise Simple harmonic oscillations for 9702 exams?

Start with the visual steps on this page, note the key exam points, then attempt a 9702 past-paper question on Simple harmonic oscillations using MarkScheme's /mark tool. Mark strictly against the official scheme and re-read any marks you lost.

MarkScheme 9702

Opening…

17.1Physics25 min readPREMIUM

Simple harmonic oscillations

Welcome to the fascinating world of Simple Harmonic Motion (SHM)! This core concept describes a specific, predictable type of oscillatory movement found everywhere, from vibrating guitar strings to the precise ticks of an old clock. You'll learn the defining characteristics of SHM, master its mathematical descriptions, and understand how energy flows within these elegant systems. This pilot aligns with Senpai Corner A Level notes (2025–2027) for topic 17.1.

BY THE END, YOU CAN…

exam checklist — tick these off

1Define and apply the conditions for Simple Harmonic Motion (SHM).
2Calculate displacement, velocity, and acceleration using SHM equations.
3Represent SHM graphically and interpret displacement-time, velocity-time, and acceleration-time graphs.
4Explain energy transformations and the effects of damping on oscillating systems.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Simple harmonic oscillations

Cambridge 9702 Paper 4 — Simple harmonic oscillations (17.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
17.1 Simple harmonic oscillations.
2
An oscillation is defined as repeated back and forth movements on either side of any equilibrium position.
3
When the object stops oscillating it returns to its equilibrium position.
4
An oscillation is a more specific term for a vibration.

What this topic covers

The official Cambridge syllabus points this lesson works through.

17.1.1
Understand and use the terms displacement, amplitude, period, frequency, angular frequency and phase difference in the context of oscillations, and express the period in terms of both frequency and angular frequency
17.1.2
Understand that simple harmonic motion occurs when acceleration is proportional to displacement from a fixed point and in the opposite direction
17.1.3
Use $a = -ω^2x$ and recall and use, as a solution to this equation, $x = x_0 \sin ωt$
17.1.4
Use the equations $v = v_0 \cos ωt$ and $v = \pm ω\sqrt{(x_0^2 - x^2)}$
17.1.5
Analyse and interpret graphical representations of the variations of displacement, velocity and acceleration for simple harmonic motion

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Figure Interactive1 / 3

Displacement x = A cos(ωt) — the mass traces a cosine curve against time.

31 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

31 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

3JCN PhysicsStart here · 19702 17.1 · 9702 17.2 · IB C.1
Simple Harmonic Motion (SHM)
Set mass, spring constant and amplitude; watch x, v, a graphs and the energy exchange of a block on a spring
Why this one: Set the block oscillating and watch the x, v and a graphs together: a is always opposite to x and largest at the ends.
Try this
1. Set mass, spring constant and amplitude and read the period from the x graph.
2. Double the amplitude and compare the period and the peak velocity.
3. Compare the x, v and a graphs: note where each crosses zero and peaks.
4. Watch the KE and PE exchange across one cycle.
Look for a is proportional to minus x, v peaks at x = 0, and the period is independent of amplitude.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 29702 17.1 · 9702 17.2 · 9702 12.1
Circular Motion & SHM Relationship
Run uniform circular motion beside its projection to see SHM as a shadow of circular motion
Why this one: Watch the shadow of circular motion trace SHM; ω and x = x₀ sin ωt come from the circle.
Try this
1. Run the circular motion and watch its projection move alongside.
2. Compare the projection's displacement with the angle turned.
Look for The projection of uniform circular motion is SHM with x = r cos ωt, so ω of the SHM equals the angular speed.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
oPhysicsStart here · 39702 17.1 · IB C.1
Oscillations
SHM related to uniform circular motion with x-t, v-t and a-t graphs toggled by checkbox
Why this one: Toggle the x–t, v–t and a–t graphs: v leads x by a quarter cycle, a is always opposite x.
Try this
1. Toggle the x-t graph and watch it against the circular motion.
2. Add the v-t graph and compare its phase.
3. Add the a-t graph.
Look for Velocity leads displacement by a quarter cycle and acceleration is in antiphase with displacement.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
PhETStart here · 49702 17.1–17.2
Masses and Springs
Hang a mass on a spring, set it bouncing and read the period, energy bars and graph.
Why this one: Turn on the velocity and acceleration arrows: acceleration always points back to equilibrium.
Try this
1. On “Lab”, hang 250 g, start it bouncing and use the timer for 10 oscillations.
2. Double the mass — T grows by √2. Stiffen the spring — T falls.
3. Show “Energy” and watch KE and PE swap while the total stays level.
Look for T = 2π√(m/k); amplitude does not change the period.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
3JCN PhysicsStart here · 59702 17.1 · 9702 17.2 · IB C.1
Simple Pendulum
Set length and amplitude of a simple pendulum; read the period and compare with the formula
Why this one: Change the length and compare the period with T = 2π√(l/g); amplitude barely matters for small swings.
Try this
1. Set a length and amplitude and read the period.
2. Quadruple the length and compare the period with the formula.
3. Change the amplitude only and compare.
Look for T = 2π√(L/g): the period doubles when the length quadruples and is independent of small amplitudes.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

More simulations26 more on this topic — core ones first

oPhysicsCore9702 17.1 · 9702 7.1 · IB C.1
Simple Harmonic Motion, Circular Motion, and Transverse Waves
Link SHM, uniform circular motion and a transverse wave side by side with sliders and checkboxes
Try this
1. Use the checkboxes to show SHM and circular motion together.
2. Change the frequency slider and watch all three panels.
3. Show the transverse wave and compare one particle with the SHM.
Look for The SHM is the projection of circular motion, and each wave particle performs the same SHM with a phase lag.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 17.1 · 9702 17.2 · IB C.1
Simple Harmonic Motion: Mass on a Spring
Mass on a horizontal spring: set initial displacement, mass and k; step through motion with x, v, a graphs
Try this
1. Set an initial displacement and step through one period.
2. Double the mass and compare the period.
3. Double k instead and compare again.
Look for Acceleration is always opposite to displacement, and the period grows with mass and shrinks with spring constant.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 17.1 · IB C.1
Oscillation Graphs Quiz
Quiz: match or interpret displacement/velocity/acceleration graphs of an oscillator
Try this
1. Work through one question and check the answer.
2. Identify which graph is the gradient of which.
3. Try another question.
Look for Velocity is zero where displacement is largest, and the acceleration graph is the displacement graph inverted.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 17.1 · IB C.1
Simple Harmonic Motion Tutorial
Step-by-step tutorial on SHM with embedded interactive panels (Next/Back navigation)
Try this
1. Step through the tutorial with Next.
2. Use the interactive panel on each page before moving on.
3. Go Back to recheck a definition.
Look for Acceleration in SHM is proportional to displacement and directed towards equilibrium.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 17.1 · 9702 7.1 · IB C.1
Oscillations and Phase Shift
Compare two SHM oscillators / waves with an adjustable phase shift between them
Try this
1. Set the phase shift to zero and compare the two oscillators.
2. Set it to a quarter cycle (90°).
3. Set it to half a cycle (180°).
Look for At 180° the oscillators are in antiphase, moving in opposite directions at every instant.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
The Physics ClassroomCore9702 7.1 · 9702 17.1 · IB C.2
Transverse Sine Wave Maker
A marker on a turntable oscillates one cycle per turn and traces a sine wave, with 3D viewing
Try this
1. Run the turntable and watch the trace.
2. Compare one turn with one cycle of the trace.
3. Change the 3D view.
Look for One rotation of the turntable produces one wavelength of the trace.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$a = -\omega^2 x$

Tap a symbol — great for exam definitions

KEY RELATION

$x = x_0 \sin(\omega t)$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

The Defining Principle: What is SHM?

Simple Harmonic Motion isn't just any wobble or swing. It's a very specific oscillation where the force trying to restore the object to its central, balanced position gets stronger the further it moves away. This means its acceleration is always directed towards the equilibrium and directly proportional to how far it's been displaced.

$a = -\omega^2 x$

17.1 Simple harmonic oscillations.
An oscillation is defined as repeated back and forth movements on either side of any equilibrium position.
When the object stops oscillating it returns to its equilibrium position.
An oscillation is a more specific term for a vibration.
An oscillator is a device that works on the principles of oscillations.
Oscillating systems can be represented by displacement-time graphics.

Not clear?

Essential Vocabulary for Oscillations

Before diving into complex equations, it's crucial to grasp the fundamental terms that describe any oscillation, especially SHM. These terms provide the language to quantify and understand the rhythmic dance of an object.

Displacement (x): Instantaneous distance from equilibrium.
Amplitude ( $x_0$ or A): Maximum displacement from equilibrium.
Period (T): Time for one complete oscillation cycle (in seconds).
Frequency (f): Number of cycles per second ( $f = 1/T$ , in Hertz).
Angular Frequency ( $\omega$ ): Rate of change of phase angle ( $\omega = 2\pi f = 2\pi/T$ , in rad/s).

Not clear?

Describing Motion: Displacement, Velocity, and Acceleration

Since SHM is so predictable, we can use mathematical models to perfectly describe an object's position, speed, and how fast it's speeding up or slowing down at any moment. These equations are fundamental for solving SHM problems.

$x = x_0 \sin(\omega t)$ or $x = x_0 \cos(\omega t)$

The displacement equation describes the object's position at time 't'. Remember, sine and cosine functions are periodic, reflecting the oscillating nature. From this, we can derive velocity and acceleration:

Velocity (v): Rate of change of displacement.
Maximum velocity ( $v_0 = \omega x_0$ ) occurs at equilibrium ( $x=0$ ).
Velocity can be found using $v = \pm \omega \sqrt{x_0^2 - x^2}$ .
Acceleration (a): Rate of change of velocity, $a = -\omega^2 x$ .

Not clear?

Phase Differences: Timing the Motion

In SHM, displacement, velocity, and acceleration are all linked, but they don't peak or trough at the exact same time. Their 'phase difference' describes how much one quantity lags or leads another in the oscillation cycle.

Displacement and Acceleration: $180^\circ$ ( $\pi$ radians) out of phase. When x is max positive, a is max negative.
Displacement and Velocity: $90^\circ$ ( $\pi/2$ radians) out of phase. When x is max, v is zero; when x is zero, v is max.
In Phase: Two oscillations move together, peaking and troughing at the same time (phase difference = $2\pi n$ ).
Completely Out of Phase: Two oscillations move exactly opposite (phase difference = $(2n+1)\pi$ ).

Not clear?

Graphical Representation of SHM

The sinusoidal nature of SHM is best visualized through graphs of displacement, velocity, and acceleration against time. These graphs clearly show the amplitude, period, and phase relationships between the different quantities.

Displacement-time (x-t) graph: A sine or cosine curve. The peak value is the amplitude ( $x_0$ ), and the time for one full wave is the period (T).
Velocity-time (v-t) graph: Also a sinusoidal curve, representing the gradient of the x-t graph. It leads the displacement by $90^\circ$ ( $\pi/2$ radians). When displacement is zero, velocity is maximum or minimum.
Acceleration-time (a-t) graph: Another sinusoidal curve, representing the gradient of the v-t graph. It is $180^\circ$ ( $\pi$ radians) out of phase with displacement, meaning it's an inverted version of the x-t graph (scaled by $\omega^2$ ).
Energy-displacement graph: A graph of energy vs. displacement shows a constant total energy line, a parabola for potential energy ( $E_P \propto x^2$ ), and an inverted parabola for kinetic energy.

Not clear?

Energy Transformations in SHM

In an ideal SHM system, energy is constantly swapping between kinetic (due to motion) and potential (due to position). The total mechanical energy, however, remains perfectly conserved, assuming no external losses.

Kinetic Energy (KE): Energy of motion, maximal at the equilibrium position ( $x=0$ ). Given by $E_K = \frac{1}{2} m \omega^2 (x_0^2 - x^2)$ .
Potential Energy (PE): Stored energy, maximal at the amplitude positions ( $x=\pm x_0$ ). Given by $E_P = \frac{1}{2} m \omega^2 x^2$ .
Energy Conservation: As the oscillator moves, energy continuously transforms between KE and PE, but their sum, the total energy, remains constant.
Total Energy ( $E_{total}$ ): The sum $E_K + E_P$ is always constant and equals the maximum potential or kinetic energy: $E_{total} = \frac{1}{2} m \omega^2 x_0^2$ .

Not clear?

Damping: When Oscillations Fade

In reality, no system oscillates forever. Damping is the process where energy is gradually lost from an oscillating system, usually converted into heat or sound, causing the amplitude of the oscillations to decrease over time until the motion stops.

Free Oscillations: Oscillations without any external driving force, at a system's natural frequency.
Underdamping (Light Damping): Amplitude slowly decays over many cycles, like a swinging pendulum.
Critical Damping: System returns to equilibrium in the shortest time possible without oscillating. Ideal for car suspensions.
Overdamping (Heavy Damping): Damping is too strong, causing a slow return to equilibrium than critical damping, also without oscillating.

EXAM TIP

Pay close attention to units in SHM calculations! Angular frequency should be in rad/s, time in seconds, displacement/amplitude in metres. A common error is mixing up degrees and radians for phase calculations.

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A mass oscillating with SHM has an amplitude of 5.0 cm and a period of 1.2 s. Calculate its angular frequency, maximum velocity, and acceleration when its displacement is 3.0 cm.

1
**Step 1: $Calculate angular frequency ($ \omega $).**$ The formula is $\omega = 2\pi / T$ . $\omega = 2\pi / 1.2 \text{ s} \approx 5.236 \text{ rad/s}$ . Step 2: Calculate maximum velocity ( $v_0$ ). The formula is $v_0 = \omega x_0$ . Remember to convert amplitude to metres! $x_0 = 5.0 \text{ cm} = 0.050 \text{ m}$ . $v_0 = 5.236 \text{ rad/s} \times 0.050 \text{ m} \approx 0.2618 \text{ m/s}$ . Step 3: Calculate acceleration (a) at $x = 3.0 \text{ cm}$ . The formula is $a = -\omega^2 x$ . Convert displacement to metres. $x = 3.0 \text{ cm} = 0.030 \text{ m}$ . $a = -(5.236 \text{ rad/s})^2 \times 0.030 \text{ m} \approx -0.822 \text{ m/s}^2$ .

DONE

EXAMPLE 2

A 0.50 kg mass is attached to a spring and oscillates with SHM. The amplitude of the oscillation is 10 cm, and the period is 0.80 s. Calculate: a) The total energy of the system. b) The kinetic energy of the mass when its displacement is 6.0 cm from the equilibrium position.

1
**Step 1: $Calculate angular frequency ($ \omega $).**$ The relationship between period T and angular frequency $\omega is$ \omega = 2\pi / T$$. $\omega = 2\pi / 0.80 \text{ s} = 7.854 \text{ rad/s}$ .

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEASimple harmonic oscillations

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

Damping: In reality, no system oscillates forever. Damping is the process where energy is gradually lost from an oscillating system, usually converted into heat or sound, causing the amplitude of the oscillations to decrease over time until the motion stops.
defining relationship: Acceleration is directly proportional to displacement from equilibrium and acts in the opposite direction ( $a \propto -x$ ).}

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

Teach it back

If you can explain it simply, you own it — gaps here are marks you’d lose.

Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 10 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

17.1 Simple harmonic oscillations.
An oscillation is defined as repeated back and forth movements on either side of any equilibrium position.
When the object stops oscillating it returns to its equilibrium position.
An oscillation is a more specific term for a vibration.
An oscillator is a device that works on the principles of oscillations.
Oscillating systems can be represented by displacement-time graphics.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q4(a)

PhysicsMay/June 2024

(a)

Explain how Fig. 4.2 shows that the oscillations of the block are simple harmonic.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Question 2 of 29702/42 · Q4(b)(ii)

PhysicsMay/June 2024

(b) (ii)

the maximum speed v₀ of the oscillations

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

What makes an oscillation 'simple harmonic'?

How does energy change during Simple Harmonic Motion?

What is the difference between underdamping, critical damping, and overdamping?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q4(a) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS16.2 The first law of thermodynamics NEXT →17.2 Energy in simple harmonic motion

Discuss Simple harmonic oscillations

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Revise Simple harmonic oscillations for Cambridge 9702 (17.1)

Looking for free Physics 9702 notes on Simple harmonic oscillations? This A-Level lesson covers official syllabus point 17.1 on Paper 4: A Level Structured Questions. Use the visual steps, key terms, and quick checks below — then practise a real 9702 past-paper question with mark-scheme marking. Built for students searching "Simple harmonic oscillations 9702 revision", "9702 17.1 notes", or a free alternative to paid note sites.

Full Physics 9702 course Mark a past paper →9702 subject hub

17.1Physics25 min readPREMIUM

Simple harmonic oscillations

BY THE END, YOU CAN…

exam checklist — tick these off

1Define and apply the conditions for Simple Harmonic Motion (SHM).
2Calculate displacement, velocity, and acceleration using SHM equations.
3Represent SHM graphically and interpret displacement-time, velocity-time, and acceleration-time graphs.
4Explain energy transformations and the effects of damping on oscillating systems.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Simple harmonic oscillations

Cambridge 9702 Paper 4 — Simple harmonic oscillations (17.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
17.1 Simple harmonic oscillations.
2
An oscillation is defined as repeated back and forth movements on either side of any equilibrium position.
3
When the object stops oscillating it returns to its equilibrium position.
4
An oscillation is a more specific term for a vibration.

What this topic covers

The official Cambridge syllabus points this lesson works through.

17.1.1
Understand and use the terms displacement, amplitude, period, frequency, angular frequency and phase difference in the context of oscillations, and express the period in terms of both frequency and angular frequency
17.1.2
Understand that simple harmonic motion occurs when acceleration is proportional to displacement from a fixed point and in the opposite direction
17.1.3
Use $a = -ω^2x$ and recall and use, as a solution to this equation, $x = x_0 \sin ωt$
17.1.4
Use the equations $v = v_0 \cos ωt$ and $v = \pm ω\sqrt{(x_0^2 - x^2)}$
17.1.5
Analyse and interpret graphical representations of the variations of displacement, velocity and acceleration for simple harmonic motion

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Figure Interactive1 / 3

Displacement x = A cos(ωt) — the mass traces a cosine curve against time.

31 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

31 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

3JCN PhysicsStart here · 19702 17.1 · 9702 17.2 · IB C.1
Simple Harmonic Motion (SHM)
Set mass, spring constant and amplitude; watch x, v, a graphs and the energy exchange of a block on a spring
Why this one: Set the block oscillating and watch the x, v and a graphs together: a is always opposite to x and largest at the ends.
Try this
1. Set mass, spring constant and amplitude and read the period from the x graph.
2. Double the amplitude and compare the period and the peak velocity.
3. Compare the x, v and a graphs: note where each crosses zero and peaks.
4. Watch the KE and PE exchange across one cycle.
Look for a is proportional to minus x, v peaks at x = 0, and the period is independent of amplitude.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 29702 17.1 · 9702 17.2 · 9702 12.1
Circular Motion & SHM Relationship
Run uniform circular motion beside its projection to see SHM as a shadow of circular motion
Why this one: Watch the shadow of circular motion trace SHM; ω and x = x₀ sin ωt come from the circle.
Try this
1. Run the circular motion and watch its projection move alongside.
2. Compare the projection's displacement with the angle turned.
Look for The projection of uniform circular motion is SHM with x = r cos ωt, so ω of the SHM equals the angular speed.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
oPhysicsStart here · 39702 17.1 · IB C.1
Oscillations
SHM related to uniform circular motion with x-t, v-t and a-t graphs toggled by checkbox
Why this one: Toggle the x–t, v–t and a–t graphs: v leads x by a quarter cycle, a is always opposite x.
Try this
1. Toggle the x-t graph and watch it against the circular motion.
2. Add the v-t graph and compare its phase.
3. Add the a-t graph.
Look for Velocity leads displacement by a quarter cycle and acceleration is in antiphase with displacement.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
PhETStart here · 49702 17.1–17.2
Masses and Springs
Hang a mass on a spring, set it bouncing and read the period, energy bars and graph.
Why this one: Turn on the velocity and acceleration arrows: acceleration always points back to equilibrium.
Try this
1. On “Lab”, hang 250 g, start it bouncing and use the timer for 10 oscillations.
2. Double the mass — T grows by √2. Stiffen the spring — T falls.
3. Show “Energy” and watch KE and PE swap while the total stays level.
Look for T = 2π√(m/k); amplitude does not change the period.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
3JCN PhysicsStart here · 59702 17.1 · 9702 17.2 · IB C.1
Simple Pendulum
Set length and amplitude of a simple pendulum; read the period and compare with the formula
Why this one: Change the length and compare the period with T = 2π√(l/g); amplitude barely matters for small swings.
Try this
1. Set a length and amplitude and read the period.
2. Quadruple the length and compare the period with the formula.
3. Change the amplitude only and compare.
Look for T = 2π√(L/g): the period doubles when the length quadruples and is independent of small amplitudes.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

More simulations26 more on this topic — core ones first

oPhysicsCore9702 17.1 · 9702 7.1 · IB C.1
Simple Harmonic Motion, Circular Motion, and Transverse Waves
Link SHM, uniform circular motion and a transverse wave side by side with sliders and checkboxes
Try this
1. Use the checkboxes to show SHM and circular motion together.
2. Change the frequency slider and watch all three panels.
3. Show the transverse wave and compare one particle with the SHM.
Look for The SHM is the projection of circular motion, and each wave particle performs the same SHM with a phase lag.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 17.1 · 9702 17.2 · IB C.1
Simple Harmonic Motion: Mass on a Spring
Mass on a horizontal spring: set initial displacement, mass and k; step through motion with x, v, a graphs
Try this
1. Set an initial displacement and step through one period.
2. Double the mass and compare the period.
3. Double k instead and compare again.
Look for Acceleration is always opposite to displacement, and the period grows with mass and shrinks with spring constant.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 17.1 · IB C.1
Oscillation Graphs Quiz
Quiz: match or interpret displacement/velocity/acceleration graphs of an oscillator
Try this
1. Work through one question and check the answer.
2. Identify which graph is the gradient of which.
3. Try another question.
Look for Velocity is zero where displacement is largest, and the acceleration graph is the displacement graph inverted.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 17.1 · IB C.1
Simple Harmonic Motion Tutorial
Step-by-step tutorial on SHM with embedded interactive panels (Next/Back navigation)
Try this
1. Step through the tutorial with Next.
2. Use the interactive panel on each page before moving on.
3. Go Back to recheck a definition.
Look for Acceleration in SHM is proportional to displacement and directed towards equilibrium.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
oPhysicsCore9702 17.1 · 9702 7.1 · IB C.1
Oscillations and Phase Shift
Compare two SHM oscillators / waves with an adjustable phase shift between them
Try this
1. Set the phase shift to zero and compare the two oscillators.
2. Set it to a quarter cycle (90°).
3. Set it to half a cycle (180°).
Look for At 180° the oscillators are in antiphase, moving in opposite directions at every instant.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
The Physics ClassroomCore9702 7.1 · 9702 17.1 · IB C.2
Transverse Sine Wave Maker
A marker on a turntable oscillates one cycle per turn and traces a sine wave, with 3D viewing
Try this
1. Run the turntable and watch the trace.
2. Compare one turn with one cycle of the trace.
3. Change the 3D view.
Look for One rotation of the turntable produces one wavelength of the trace.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$a = -\omega^2 x$

Tap a symbol — great for exam definitions

KEY RELATION

$x = x_0 \sin(\omega t)$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

The Defining Principle: What is SHM?

$a = -\omega^2 x$

17.1 Simple harmonic oscillations.
An oscillation is defined as repeated back and forth movements on either side of any equilibrium position.
When the object stops oscillating it returns to its equilibrium position.
An oscillation is a more specific term for a vibration.
An oscillator is a device that works on the principles of oscillations.
Oscillating systems can be represented by displacement-time graphics.

Not clear?

Essential Vocabulary for Oscillations

Displacement (x): Instantaneous distance from equilibrium.
Amplitude ( $x_0$ or A): Maximum displacement from equilibrium.
Period (T): Time for one complete oscillation cycle (in seconds).
Frequency (f): Number of cycles per second ( $f = 1/T$ , in Hertz).
Angular Frequency ( $\omega$ ): Rate of change of phase angle ( $\omega = 2\pi f = 2\pi/T$ , in rad/s).

Not clear?

Describing Motion: Displacement, Velocity, and Acceleration

$x = x_0 \sin(\omega t)$ or $x = x_0 \cos(\omega t)$

Velocity (v): Rate of change of displacement.
Maximum velocity ( $v_0 = \omega x_0$ ) occurs at equilibrium ( $x=0$ ).
Velocity can be found using $v = \pm \omega \sqrt{x_0^2 - x^2}$ .
Acceleration (a): Rate of change of velocity, $a = -\omega^2 x$ .

Not clear?

Phase Differences: Timing the Motion

Displacement and Acceleration: $180^\circ$ ( $\pi$ radians) out of phase. When x is max positive, a is max negative.
Displacement and Velocity: $90^\circ$ ( $\pi/2$ radians) out of phase. When x is max, v is zero; when x is zero, v is max.
In Phase: Two oscillations move together, peaking and troughing at the same time (phase difference = $2\pi n$ ).
Completely Out of Phase: Two oscillations move exactly opposite (phase difference = $(2n+1)\pi$ ).

Not clear?

Graphical Representation of SHM

Displacement-time (x-t) graph: A sine or cosine curve. The peak value is the amplitude ( $x_0$ ), and the time for one full wave is the period (T).
Velocity-time (v-t) graph: Also a sinusoidal curve, representing the gradient of the x-t graph. It leads the displacement by $90^\circ$ ( $\pi/2$ radians). When displacement is zero, velocity is maximum or minimum.
Acceleration-time (a-t) graph: Another sinusoidal curve, representing the gradient of the v-t graph. It is $180^\circ$ ( $\pi$ radians) out of phase with displacement, meaning it's an inverted version of the x-t graph (scaled by $\omega^2$ ).
Energy-displacement graph: A graph of energy vs. displacement shows a constant total energy line, a parabola for potential energy ( $E_P \propto x^2$ ), and an inverted parabola for kinetic energy.

Not clear?

Energy Transformations in SHM

Kinetic Energy (KE): Energy of motion, maximal at the equilibrium position ( $x=0$ ). Given by $E_K = \frac{1}{2} m \omega^2 (x_0^2 - x^2)$ .
Potential Energy (PE): Stored energy, maximal at the amplitude positions ( $x=\pm x_0$ ). Given by $E_P = \frac{1}{2} m \omega^2 x^2$ .
Energy Conservation: As the oscillator moves, energy continuously transforms between KE and PE, but their sum, the total energy, remains constant.
Total Energy ( $E_{total}$ ): The sum $E_K + E_P$ is always constant and equals the maximum potential or kinetic energy: $E_{total} = \frac{1}{2} m \omega^2 x_0^2$ .

Not clear?

Damping: When Oscillations Fade

Free Oscillations: Oscillations without any external driving force, at a system's natural frequency.
Underdamping (Light Damping): Amplitude slowly decays over many cycles, like a swinging pendulum.
Critical Damping: System returns to equilibrium in the shortest time possible without oscillating. Ideal for car suspensions.
Overdamping (Heavy Damping): Damping is too strong, causing a slow return to equilibrium than critical damping, also without oscillating.

EXAM TIP

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A mass oscillating with SHM has an amplitude of 5.0 cm and a period of 1.2 s. Calculate its angular frequency, maximum velocity, and acceleration when its displacement is 3.0 cm.

1
**Step 1: $Calculate angular frequency ($ \omega $).**$ The formula is $\omega = 2\pi / T$ . $\omega = 2\pi / 1.2 \text{ s} \approx 5.236 \text{ rad/s}$ . Step 2: Calculate maximum velocity ( $v_0$ ). The formula is $v_0 = \omega x_0$ . Remember to convert amplitude to metres! $x_0 = 5.0 \text{ cm} = 0.050 \text{ m}$ . $v_0 = 5.236 \text{ rad/s} \times 0.050 \text{ m} \approx 0.2618 \text{ m/s}$ . Step 3: Calculate acceleration (a) at $x = 3.0 \text{ cm}$ . The formula is $a = -\omega^2 x$ . Convert displacement to metres. $x = 3.0 \text{ cm} = 0.030 \text{ m}$ . $a = -(5.236 \text{ rad/s})^2 \times 0.030 \text{ m} \approx -0.822 \text{ m/s}^2$ .

DONE

EXAMPLE 2

1
**Step 1: $Calculate angular frequency ($ \omega $).**$ The relationship between period T and angular frequency $\omega is$ \omega = 2\pi / T$$. $\omega = 2\pi / 0.80 \text{ s} = 7.854 \text{ rad/s}$ .

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEASimple harmonic oscillations

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

Damping: In reality, no system oscillates forever. Damping is the process where energy is gradually lost from an oscillating system, usually converted into heat or sound, causing the amplitude of the oscillations to decrease over time until the motion stops.
defining relationship: Acceleration is directly proportional to displacement from equilibrium and acts in the opposite direction ( $a \propto -x$ ).}

10Apply

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0 of 6 answered

11Understand

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Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

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Your guess — write it before you look

1 / 10 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

17.1 Simple harmonic oscillations.
An oscillation is defined as repeated back and forth movements on either side of any equilibrium position.
When the object stops oscillating it returns to its equilibrium position.
An oscillation is a more specific term for a vibration.
An oscillator is a device that works on the principles of oscillations.
Oscillating systems can be represented by displacement-time graphics.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q4(a)

PhysicsMay/June 2024

(a)

Explain how Fig. 4.2 shows that the oscillations of the block are simple harmonic.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Question 2 of 29702/42 · Q4(b)(ii)

PhysicsMay/June 2024

(b) (ii)

the maximum speed v₀ of the oscillations

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

What makes an oscillation 'simple harmonic'?

How does energy change during Simple Harmonic Motion?

What is the difference between underdamping, critical damping, and overdamping?

Checkpoint

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Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q4(a) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

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Discuss Simple harmonic oscillations

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Revise Simple harmonic oscillations for Cambridge 9702 (17.1)

In simple terms

What this topic covers

Explore the concept

Simulations

Simple Harmonic Motion (SHM)

Circular Motion & SHM Relationship

Oscillations

Masses and Springs

Simple Pendulum

Simple Harmonic Motion, Circular Motion, and Transverse Waves

Simple Harmonic Motion: Mass on a Spring

Oscillation Graphs Quiz

Simple Harmonic Motion Tutorial

Oscillations and Phase Shift

Transverse Sine Wave Maker

Key formulas

Full topic notes

The Defining Principle: What is SHM?

Essential Vocabulary for Oscillations

Describing Motion: Displacement, Velocity, and Acceleration

Phase Differences: Timing the Motion

Graphical Representation of SHM

Energy Transformations in SHM

Damping: When Oscillations Fade

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Simple harmonic oscillations

Revise Simple harmonic oscillations for Cambridge 9702 (17.1)

In simple terms

What this topic covers

Explore the concept

Simulations

Simple Harmonic Motion (SHM)

Circular Motion & SHM Relationship

Oscillations

Masses and Springs

Simple Pendulum

Simple Harmonic Motion, Circular Motion, and Transverse Waves

Simple Harmonic Motion: Mass on a Spring

Oscillation Graphs Quiz

Simple Harmonic Motion Tutorial

Oscillations and Phase Shift

Transverse Sine Wave Maker

Key formulas

Full topic notes

The Defining Principle: What is SHM?

Essential Vocabulary for Oscillations

Describing Motion: Displacement, Velocity, and Acceleration

Phase Differences: Timing the Motion

Graphical Representation of SHM

Energy Transformations in SHM

Damping: When Oscillations Fade

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Simple harmonic oscillations