What sets a pendulum's period?
T = 2π√(L/g): only the length L and gravity g (9.81 m/s²). Mass does not matter, and for small swings neither does the amplitude — which is why pendulum clocks keep time.
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Pendulum Period & Swing
Find a pendulum's period T = 2π√(L/g) and its angle θ(t) = θ₀·cos(2πt/T) at any time, with angles in degrees or radians.
T = 2π√(L/g); θ(t) = θ₀·cos(2πt/T)
Angle unit
Frequently asked questions
How does the angle change over time?
For small swings, θ(t) = θ₀·cos(2πt/T) — simple harmonic motion, starting at θ₀ and swinging symmetrically.
Can you show a worked example?
A 1 m pendulum has T = 2π√(1/9.81) ≈ 2.006 s. Starting at 10°, after 0.5 s it has nearly reached the far side.
Why does it say 'small angle'?
The formula relies on sinθ ≈ θ in radians, valid for small swings. Beyond about 20° the true period grows slightly longer than 2π√(L/g).
Degrees or radians?
The swing angle can be entered and shown in either; 10° is about 0.1745 rad.