IB Physics Simple Harmonic Motion (SHM): FAQs

SHM is periodic motion where acceleration stays proportional to displacement from equilibrium and always points back towards it — defined by a = -ω²x. According to the IB's 2025 Physics guide, it sits in Topic C.1 (Wave behaviour) and is examined across Paper 1, Paper 2 and Paper 3, at both SL and HL.

The defining equation is a = -ω²x, given on the data booklet. Its solutions are x = x₀cos(ωt) or x = x₀sin(ωt), depending on where the object starts. Velocity is v = ±ω√(x₀² - x²), and ω = 2π/T = 2πf — you don't need to derive these, just apply them correctly.

Not every repeating motion is SHM. Any back-and-forth motion counts as an oscillation, but SHM specifically requires the restoring force — and therefore acceleration — to be proportional to displacement and directed towards equilibrium. A pendulum swinging at large angles or a bouncing ball are oscillations, but not true SHM.

Velocity leads displacement by a quarter cycle (90°), and acceleration is exactly out of phase with displacement (180°). When displacement is at its maximum, velocity is zero and acceleration is maximum but pointing the opposite way. Sketching one graph from another is a classic Paper 2 question.

The most common error I see is mixing up the sine and cosine solutions depending on the starting position, or forgetting ω = 2πf. Markers also cut marks when students state 'acceleration is proportional to displacement' without adding the direction — IB mark schemes specifically want 'towards equilibrium' or the negative sign included.

SHM sits at mid-difficulty. The core equations are handed to you on the data booklet, but questions combine algebra, graph reading and energy reasoning, which catches out students who've only memorised formulas without understanding the phase relationships. HL adds damped and forced oscillations, which raises the demand further.

Yes. Paper 1 tests SHM through multiple-choice conceptual and short calculation questions. Paper 2 includes extended calculations and graph-based questions, often combined with waves or energy transfer. Paper 3 can bring SHM into the experimental/data-based section, particularly through pendulum or spring practicals with real measurement uncertainty.

For a mass-spring system, T = 2π√(m/k); for a simple pendulum, T = 2π√(L/g) — both formulas are on the data booklet. Substitute carefully, keep every value in SI units, and remember that for true SHM, period doesn't depend on amplitude.

Total energy in SHM stays constant, but it's continuously exchanged between kinetic and potential forms. Kinetic energy is maximum at equilibrium (x = 0) and zero at maximum displacement, while potential energy does exactly the opposite. Total energy is E = ½kx₀², using amplitude x₀ and the system's spring constant.

A travelling wave is really a chain of points, each undergoing SHM, which is why the same ω, T and f definitions carry straight across into wave theory. At HL, SHM also underpins forced oscillations and resonance — when a driving frequency matches a system's natural frequency, amplitude grows sharply.

SL students need the definition, core equations, graphs and energy exchange in SHM. HL students additionally cover damped and forced oscillations, resonance, and the effect of driving frequency on amplitude. According to the IB's 2025 Physics guide, this HL-only extension sits within the Wave behaviour strand, alongside forced oscillations.

Start with past-paper questions tagged Wave behaviour or SHM specifically, since examiners tend to reuse similar graph-reading and calculation styles year to year. On RevisionPrep, students use topical worksheets and revision notes covering SHM alongside full past-paper mock sets, which builds both formula fluency and confidence reading unfamiliar graphs.