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Simple pendulum
Beginner
A small mass on a light string.
T = 2π√(L/g)A mass m on a light string of length L: T = 2π√(L/g) for small angles. The period is independent of the mass.
L = 1 m: T = 2.0 s.
Do not use for large angles or physical pendulums.
In more detail
A simple pendulum is a mass on a light string swinging under gravity. For small angles it performs SHM with period T = 2π sqrt(L/g), independent of the mass.
Real-world uses
- Pendulum clocks use the regular period to keep time.
- Seismometers use pendulum-like motion to detect ground vibrations.
- Early clocks used pendulums, whose swing period depends on the length and the local gravity.
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Frequently asked questions
Does the mass matter?
No. The period depends on the length and g, not the mass.
Why must the angle be small?
Because the restoring force is only approximately proportional to displacement for small angles.
Does the mass of the bob affect the period?
No. For a simple pendulum, the period depends only on the length and g, so a heavy and a light bob swing in the same time.
Related topics in Oscillations & SHM
Mass–spring system · Vertical spring · Springs in series/parallel oscillations · Small-angle approximation · Pendulum at large amplitude · Physical pendulum