Pendulum Period Calculator
Compute the swing period and frequency of a simple pendulum from its length and local gravity — the formula that ran clocks for 300 years.
Period (small-angle)
2.01
Breakdown
- Period with amplitude correction
- 2.01
- Amplitude adds (%)
- 0.19
- Frequency (Hz)
- 0.50
- Swings per minute
- 29.91
- Length for 1 s period (m)
- 0.25
- Max speed at bottom (m/s)
- 0.55
Last updated:
FAQ
Does the bob's mass affect the period?
No — a lead ball and a cork ball of identical length swing at the same rate. Gravity pulls harder on heavier bobs but inertia resists proportionally more, and the two effects cancel exactly. That's why T = 2π√(L/g) has no m in it.
Why does amplitude appear in the results?
The textbook formula assumes tiny swings. At larger angles the restoring force weakens relative to the arc, slowing the pendulum — about 0.2% at 10°, 1.7% at 30°. The corrected figure uses an elliptic-integral expansion for honest large-swing numbers.
How did pendulums keep clocks accurate?
A one-second period needs a length of about 0.994 m at Earth's gravity — the 'seconds pendulum' that defined early timekeeping. Because g varies slightly with latitude and altitude, pendulum clocks gain or lose minutes per month when moved, which first revealed Earth's bulge.
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