Formulas & tables/Physics/Oscillations/Period of a simple pendulum

Period of a simple pendulum

T=2πLgT=2\pi\sqrt{\dfrac{L}{g}}

Result unit: s (second)

What it describes

The time of one full swing of a simple pendulum; it depends only on the length and the gravitational acceleration — not on the mass or the amplitude.

Symbols

TT
period of oscillation
[s]
LL
length of the pendulum
[m]
gg
gravitational acceleration
[m/s²]

Where it comes from

The period depends only on the length and on gg, not on the mass nor (for small displacements) on the amplitude — this is the isochronism of the pendulum. A longer pendulum swings more slowly.

When to use it

A simple pendulum at small displacements; determining gg.

Example

Calculate the period of a pendulum of length 1 m (g=9.8g=9.8).
SubstitutionL=1L=1 m, g=9.8g=9.8.
ResultT=2π1/9.8≈2.0T=2\pi\sqrt{1/9.8}\approx2.0 s.

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