A Level Oscillations Hub

A Level Physics oscillations hub: Simple Harmonic Motion (SHM), equations, graphs, energy, damping, and resonance.

  • GCE A-Level H2 Physics 2027
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.

Start here

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.

  1. Free oscillations, investigation and quantities
  2. SHM definition, equations, graphs and phase
  3. Energy interchange and damping
  4. Forced oscillations, resonance and response
  5. Periodic Motion

    Describe free oscillations, define period, frequency, angular frequency and phase, and plan reliable timing measurements (A Level Physics).

  6. Simple Harmonic Motion

    Use the defining equation a = −ω²x, apply SHM displacement/velocity relations, and describe energy changes in SHM (A Level Physics).

  7. 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).

  8. Damping

    Describe damping as energy loss in oscillations, compare light/critical/heavy damping, and explain why critical damping is useful (A Level Physics).

  9. Natural Frequency

    Define natural and driving frequency, distinguish free from forced oscillations, and identify the steady forced-response frequency (A Level Physics).

  10. Resonance

    Explain resonance using forced oscillations, interpret amplitude–frequency response curves, and discuss useful vs dangerous resonance (A Level Physics).

  11. Questions for Oscillations (JC) Set 1

    A Level Physics oscillations practice questions (JC Set 1), with worked answers.

Revision

Quick reference
Quantity or ideaRelationshipCheck
Period and frequencyT = 1/fOne cycle takes time T
Angular frequencyω = 2π f = 2π/TUse radians
SHM definitiona = -ω²xAcceleration points towards equilibrium
Displacement modelx = x₀ sin(ω t + φ)φ sets the initial state
Speed at displacementv = ±ω square root of (x₀²-x²)Sign gives direction
Ideal SHM energyE = (1/2)mω²x₀²Constant 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

  1. Define signed displacement x from equilibrium.
  2. Find the resultant restoring force or acceleration.
  3. Rearrange to a = -kx, where k is a positive constant.
  4. Identify k = ω² and state that acceleration is proportional and opposite to displacement.

Read SHM graphs

  1. Mark equilibrium and both extremes.
  2. Use the gradient of an x–t graph for velocity.
  3. Use a = -ω²x for the acceleration sign.
  4. Check that v leads x by π/2 and a is π out of phase with x.

Describe resonance

  1. Name the driving frequency and natural frequency separately.
  2. Locate resonance at the maximum steady-state amplitude, close to or at the natural frequency.
  3. State that more damping lowers and broadens the response peak.
Top exam traps
  1. Periodic is not automatically SHM: SHM requires a ∝ -x.
  2. Free does not mean force-free: a restoring force acts; there is no periodic driver.
  3. Speed and acceleration maxima occur at different places: speed at equilibrium, acceleration magnitude at the extremes.
  4. Forced frequency: after transients decay, the oscillator follows the driving frequency.
  5. Critical versus heavy damping: both are non-oscillatory, but critical damping settles fastest.

Practice

Quiz and structured 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

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Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027