`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.

The Math / Science

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

See also

• 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

Reference

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