A Level Oscillations Hub
A Level Physics oscillations hub: Simple Harmonic Motion (SHM), equations, graphs, energy, damping, and resonance.
Learning goals
- Use oscillation quantities and describe free oscillations and their investigation.
- Relate displacement, velocity, acceleration and phase in simple harmonic motion.
- Identify and analyse simple harmonic motion using its defining equation and sinusoidal solutions.
- Describe kinetic–potential energy interchange in ideal simple harmonic motion.
- Compare light, critical and heavy damping and explain critical-damping applications.
- Distinguish free and forced oscillations, natural frequency and driving frequency.
- Interpret resonance response curves, damping effects and practical applications.
Oscillations connect periodic timing to restoring forces, phase, energy transfer, damping and resonance. The central decision is whether the motion satisfies the SHM condition a = -ω²x; periodic motion alone is not enough.
Understand first: angular frequency links this topic to Circular Motion, while energy interchange builds on Work, Energy & Power.
Common mark-loss errors: treating every repeating motion as SHM, using degrees in sin(ω t), confusing maximum acceleration with maximum speed, and saying a forced oscillator moves at its natural frequency.
Move to structured work when: you can identify the direction of x, v and a at any SHM checkpoint and describe how damping changes a resonance curve.
Lessons
Work through these lessons in order.
- Free oscillations, investigation and quantities
- SHM definition, equations, graphs and phase
- Energy interchange and damping
- Forced oscillations, resonance and response
- Periodic Motion
Describe free oscillations, define period, frequency, angular frequency and phase, and plan reliable timing measurements (A Level Physics).
- Simple Harmonic Motion
Use the defining equation a = −ω²x, apply SHM displacement/velocity relations, and describe energy changes in SHM (A Level Physics).
- SHM Graphs (Displacement, Velocity, Acceleration)
Use and interpret x–t, v–t and a–t relationships in simple harmonic motion, including phase and phase difference (A Level Physics).
- Damping
Describe damping as energy loss in oscillations, compare light/critical/heavy damping, and explain why critical damping is useful (A Level Physics).
- Natural Frequency
Define natural and driving frequency, distinguish free from forced oscillations, and identify the steady forced-response frequency (A Level Physics).
- Resonance
Explain resonance using forced oscillations, interpret amplitude–frequency response curves, and discuss useful vs dangerous resonance (A Level Physics).
- Questions for Oscillations (JC) Set 1
A Level Physics oscillations practice questions (JC Set 1), with worked answers.
Revision
Quick reference
| Quantity or idea | Relationship | Check |
|---|---|---|
| Period and frequency | T = 1/f | One cycle takes time T |
| Angular frequency | ω = 2π f = 2π/T | Use radians |
| SHM definition | a = -ω²x | Acceleration points towards equilibrium |
| Displacement model | x = x₀ sin(ω t + φ) | φ sets the initial state |
| Speed at displacement | v = ±ω square root of (x₀²-x²) | Sign gives direction |
| Ideal SHM energy | E = (1/2)mω²x₀² | Constant only without damping |
At equilibrium, |v| and kinetic energy are maximum while a = 0. At the extremes, v = 0 while |a| and potential energy are maximum.
Exam setup templates
Show that motion is SHM
- Define signed displacement x from equilibrium.
- Find the resultant restoring force or acceleration.
- Rearrange to a = -kx, where k is a positive constant.
- Identify k = ω² and state that acceleration is proportional and opposite to displacement.
Read SHM graphs
- Mark equilibrium and both extremes.
- Use the gradient of an x–t graph for velocity.
- Use a = -ω²x for the acceleration sign.
- Check that v leads x by π/2 and a is π out of phase with x.
Describe resonance
- Name the driving frequency and natural frequency separately.
- Locate resonance at the maximum steady-state amplitude, close to or at the natural frequency.
- State that more damping lowers and broadens the response peak.
Top exam traps
- Periodic is not automatically SHM: SHM requires a ∝ -x.
- Free does not mean force-free: a restoring force acts; there is no periodic driver.
- Speed and acceleration maxima occur at different places: speed at equilibrium, acceleration magnitude at the extremes.
- Forced frequency: after transients decay, the oscillator follows the driving frequency.
- Critical versus heavy damping: both are non-oscillatory, but critical damping settles fastest.
Practice
Start with the A Level Oscillations Quiz, then attempt the Oscillations Structured Set. Use the SHM Explorer when you need to check phase and graph relationships dynamically.
Continue learning
Next hub: Waves & Superposition
Continue with the next resource in this course.
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027