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`omega = sqrt( 9.80665 / "L" )`

Enter a value for all fields

The **Angular Frequency of a Pendulum** equation calculates the angular frequency of a simple pendulum with a small amplitude.

**INSTRUCTIONS:** Choose the preferred units and enter the following:

- (
**L**) Length of the Pendulum - (
**g**) Acceleration due to gravity

**Angular Frequency:** The calculator returns the angular frequency of the pendulum.

This comes from the equation **ω**=`sqrt(k/m)` when `k= (m*g)/L`. After substituting for **k**, we get the resulting equation of **ω**=`sqrt(g/L)`.

**g** - gravitational acceleration near whatever massive body is used in this calculation. The value defaults to the acceleration due to gravity at Earth's sea level but can be set to the gravitational acceleration for any planet or other body or for slightly different values on Earth including:

- acceleration due to gravity on Earth based on latitude (CLICK HERE)
- acceleration due to gravity on Earth based on altitude (CLICK HERE)

This equation has **g**, the gravitational acceleration as an input. It defaults to the standard gravitational acceleration value for gravity at the surface of the Earth but you may modify it to any gravity you desire. This allows the user to examine the pendulum's angular frequency on various planets or even as it would react close to a more massive body.

The answer displays in1/sec, which is equivalent to Hertz, and in this particular context actually means rotations or cycles per second.

- Angular Frequency of Pendulum [version designed specifically for problems involving the Earth's gravity approximation at sea level]
- Frequency of Pendulum
- Period of Pendulum
- Restoring Force on Pendulum
- Restoring Torque on Physical Pendulum

Young, Hugh and Freeman, Roger. University Physics With Modern Physics. Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 437, eq 13.32