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`F_theta = -( m * 9.80665 m/s^2)/ L * x `

Enter a value for all fields

The **Restoring Force on a Pendulum** calculator computes the approximate value of the restoring force on a pendulum.

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

- (
**m**) This is the mass of the pendulum - (
**L**) This is the length of the pendulum or the radius of the arc it sweeps. - (
**x**) This is the length of the arc.

**Restoring Force:** The calculator returns the Restoring Force (F_{g}) in newtons (N). However, this can be automatically converted to other force units via the pull-down menu.

This equation is derived from equation 13.30 of the Young and Freeman textbook cited. This equation will only work for the small angle approximation; i.e., cases where the angle, **θ**, is approximately the same as **sin(θ)** -- for example 0.1rad is about the same as sin(0.1) = 0.998. Because of the small angle approximation, we can substitute in x/L for sin(θ) and come out with a close approximation.

*original author: Billy*

- Angular Frequency of Pendulum (Any gravity)
- 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 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 436, eq 13.31