Pendulum Calculator
Galileo discovered that a pendulum's swing time depends only on its length, not the weight or swing angle (for small angles). This simple principle powers grandfather clocks and helped early scientists measure gravity. Enter a pendulum length to find its period (time for one complete swing) and frequency, or work backwards from a desired period.
How We Calculate This
Period T = 2π√(L/g), where L is length and g is gravitational acceleration. Length L = g(T/2π)². Frequency f = 1/T. Valid for small swing angles (under ~15°).
Frequently Asked Questions
Why doesn't the weight affect the period?
Heavier pendulums have more inertia but also more gravitational force. These effects cancel out exactly, so period depends only on length and gravity. Galileo discovered this by timing church chandeliers with his pulse.
How long is a grandfather clock pendulum?
About 99.4 cm (just under 1 metre). This gives a 2-second period, so each swing (half-period) is 1 second, making the clock "tick" once per second.
What is the Foucault pendulum?
A very long, heavy pendulum that demonstrates Earth's rotation. As Earth rotates beneath it, the pendulum's swing plane appears to rotate. The Panthéon in Paris has a famous 67-metre Foucault pendulum.
Does swing angle affect the period?
For small angles (under ~15°), no. For larger swings, the period increases slightly. The "small angle approximation" sin(θ) ≈ θ makes the maths much simpler.
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