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Isochronism
For true SHM the period is independent of amplitude — a larger swing takes the same time. Favourite true/false trap.
What this actually means
For true SHM the period does not depend on amplitude: a bigger swing travels further but moves proportionally faster, and the two effects cancel exactly.
It follows from a = −ω²x: ω is fixed by the system alone, so T = 2π/ω is fixed too, whatever x₀ is.
For pendulums this only holds inside the small-angle regime; push θ₀ large and the period starts to stretch.
Prove it — watch it be true
- Set a small θ₀, measure T; double θ₀ (still small), measure again: same T
- Now crank θ₀ large: the measured period drifts above 2π√(L/g)
- Isochronism is an SHM property, and large swings stop being SHM