Pendulum Calculator
Period T (seconds)
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Frequency (Hz)
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Angular Frequency (rad/s)
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How a Pendulum Works
A simple pendulum's period (time for one complete swing) depends only on its length and gravitational acceleration: T = 2π√(L/g). Remarkably, the period does not depend on the mass of the bob or the amplitude (for small angles less than about 15°).
The frequency (swings per second) is f = 1/T, and the angular frequency is ω = 2π/T. A 1-meter pendulum on Earth has a period of about 2.006 seconds — this is why grandfather clocks typically have meter-long pendulums.
Pendulums have been used for timekeeping since Galileo's observations in the 1580s. They're also used to measure gravitational acceleration, demonstrate conservation of energy, and even detect the Earth's rotation (Foucault pendulum).
Frequently Asked Questions
What is the pendulum period formula?
T = 2π√(L/g), where L is length and g is gravitational acceleration. A 1m pendulum on Earth has period ≈ 2.006 seconds.
Does mass affect a pendulum's period?
No. For a simple pendulum with small oscillations, the period depends only on length and gravity, not on the bob's mass.
Why do longer pendulums swing slower?
Period is proportional to √L. A pendulum 4 times longer has a period 2 times longer (√4 = 2). More length means more distance to travel.
What is a Foucault pendulum?
A long, heavy pendulum that demonstrates Earth's rotation. Its swing plane appears to rotate over hours because the Earth turns beneath it.