Simple Pendulum Calculator
Works out the swing time of a simple pendulum, or the length for a given time.
Answer
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Period, small-angle —
Length —
Frequency —
Period at this swing angle —
Longer than small-angle by — %
Assumes —
The formula
T = 2π√(L ÷ g)
Mass does not appear. The wide-swing period divides T by the arithmetic-geometric mean of 1 and cos(θ/2).
What to watch out for
Measure the length to the centre of the bob. A real pendulum with a heavy rod or large bob runs slightly differently.
Frequently Asked Questions
How long is a pendulum that takes 2 s per swing cycle?
About 0.994 m on Earth, which is why a “seconds pendulum” is close to a metre.
Does the swing angle matter?
A little. At 1 m, the period is 2.006 s for small swings and 2.087 s at 45°.