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MotionLab
A simple pendulum's period depends only on length and gravity — not mass or amplitude (for small swings).
A pendulum's period depends only on its length and local gravity — not on the mass of the bob or the amplitude of the swing (for small angles). This remarkable independence is why pendulum clocks, invented by Huygens in 1656, were the world's most accurate timekeepers for nearly 300 years.
The simple formula T = 2π√(L/g) assumes small swings (under ~15°). For larger amplitudes the period increases slightly — a full derivation requires elliptic integrals. For most practical purposes (clocks, lab experiments), the simple formula is accurate to well within 1%.
Period (s)
2.006
T = 2π√(L/g)
What you entered
Period: T = 2π√(L/g)
2π × √(1 / 9.81)= 2.0061 sFrequency: f = 1/T
1 / 2.0061= 0.4985 HzResult
Period (s): 2.006
A pendulum 1 m long has a period of 2.006 s (0.499 Hz).