Pendulum Period Calculator

Frequently Asked Questions

Does the mass of a pendulum affect its period?

No. For a simple pendulum the period depends only on length and gravity, not on the mass of the bob.

When is the pendulum period formula accurate?

It is accurate for small swings below about fifteen degrees, where the restoring force stays nearly proportional to displacement.

Provided by AllCalculators.io
Free online calculators for everyday. No registration required.

Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

JavaScript is required to use the interactive calculator above. The questions and answers below remain readable without JavaScript.

How This Calculator Works

A simple pendulum is a mass swinging on a light string under gravity. For small swings its motion is very nearly simple harmonic, and the time for one complete back-and-forth cycle depends only on the length of the string and the local strength of gravity. The mass and the size of the swing do not affect the period, a surprising fact first noted by Galileo.

Why The Period Stays Constant

Because the period is independent of amplitude for small angles, a pendulum keeps reliable time. This property made the pendulum clock the most accurate timekeeper for nearly three centuries. Longer pendulums swing more slowly, which is why a tall grandfather clock has a long pendulum tuned to a one-second beat.

Tips

The formula assumes small swing angles, under about fifteen degrees.

Period grows with the square root of length.

Lower gravity, as on the Moon, lengthens the period.

Pendulum Period Calculator

Frequently Asked Questions

Related Science Calculators