This mini-lesson covers Theme C.1 — Simple harmonic motion: the defining condition a ∝ −x, period and frequency, the pendulum and mass-spring systems, and the interchange of kinetic and potential energy.
Work through each screen, answer the questions as you go (some are reasoning, some are calculations) and collect ⭐ stars. Watch for the HL flag on higher-level extensions. Press Start when you're ready.
An object performs simple harmonic motion (SHM) when its acceleration is (i) proportional to its displacement from equilibrium and (ii) always directed back towards equilibrium.
Examples: a pendulum (small swings) and a mass on a spring. At the extremes the displacement, restoring force and acceleration are greatest; at the centre they are zero but the speed is greatest.
Period T is the time for one full oscillation; frequency f is oscillations per second. They are reciprocals: T = 1/f.
A pendulum of length L = 1.0 m, with g = 9.81 m s⁻².
T = 2π√(1.0 ÷ 9.81) = 2π × 0.319 = 2.0 s
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During SHM, energy shuttles between kinetic and potential stores while the total stays constant (ignoring damping).
A graph of KE and PE against displacement shows two parabolas that cross at x = 0; their sum is a flat line — the constant total energy.
Tap a statement on the left, then its match on the right.
SHM condition: a ∝ −x: acceleration proportional to, and opposite, displacement
Period: T = 1/f; pendulum T = 2π√(L/g); spring T = 2π√(m/k)
Energy: KE ↔ PE interchange; total constant; v max at centre, a max at extremes
Independence: pendulum period does not depend on mass or (small) amplitude
Damping: real oscillators lose energy and the amplitude decays
That completes Simple Harmonic Motion for IB Diploma Physics SL. Press Finish to see your score.
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