Mechanics

Pendulum period - formula in LaTeX

The period of a simple pendulum for small swings, up to a few degrees. It depends neither on the mass nor on the amplitude. The root is \sqrt{...}, and \dfrac forces a full-size fraction under it so L and g stay readable.

T = 2\pi\sqrt{\dfrac{L}{g}}

LaTeX code

Open in editor

$$
T = 2\pi\sqrt{\dfrac{L}{g}}
$$

Got this formula in your notes or on a whiteboard? Snap a photo and CamteX turns it into LaTeX. Try it free

What the symbols mean

$T$: period of oscillation (s)
$L$: length of the pendulum (m)
$g$: gravitational acceleration (m/s²)

A classical mechanics formula - it shows up in kinematics and dynamics problems and in physics lab reports.

Worked example

A 1 m pendulum completes one full swing in about 2 s. The result is rounded, so it is preceded by \approx rather than an equals sign.

T = 2\pi\sqrt{\dfrac{1\,\mathrm{m}}{9.81\,\mathrm{m/s^2}}} \approx 2.01\,\mathrm{s}

LaTeX commands in this formula

\pi: Greek letter pi
\sqrt: square root
\dfrac: fraction (display)

How to use this formula in LaTeX?

Copy the code with the button above - $$…$$ is centered display math.
Paste it into the CamteX editor, Overleaf or any LaTeX document.
Inside a sentence, use single $…$ instead of double.
The formula needs the amsmath package - CamteX templates include it in the preamble.

Related formulas - Mechanics

Drawing formulas is faster than typing them.

Draw a formula, table or chart - CamteX AI turns it into ready LaTeX and inserts it into your document.

Try it free