Period (small-angle)
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Pendulum Simulator
Adjust length, gravity, initial angle and damping; watch the pendulum swing and read the period live.
Frequency
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Angle
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Angular speed
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Elapsed
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Formula
Small-angle period: T = 2π · √(L / g)
Full equation of motion: θ̈ = −(g/L)·sin θ − b·θ̇
Full equation of motion: θ̈ = −(g/L)·sin θ − b·θ̇
Physics behind the pendulum
A simple pendulum is the canonical example of simple harmonic motion. For small angles, sin θ ≈ θ and the system oscillates with period T = 2π√(L/g). At larger angles the period grows slightly (up to a few percent at 30°, more at larger angles). This simulator uses the full non-linear equation of motion integrated with a symplectic velocity-Verlet scheme, so big-angle behaviour is physically correct. Damping b models friction and air resistance.
Worked example
L = 1 m, g = 9.80665
T = 2π · √(1/9.80665) ≈ 2.006 s
Related tools
FAQs
Small-angle period?
T = 2π·√(L/g).
Does mass affect it?
No — length and gravity only.