Restoring Force on Pendulum (Approximation)

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

Enter a value for all fields

The Restoring Force on a Pendulum calculator estimates the force to restore a pendulum.

INSTRUCTIONS: Choose your preferred units and enter the following:

(m) This is the mass of the pendulum
(L) The radius (length of the pendulum)
(x) The length of the arc swept by the pendulum

Restoring Force: The calculator returns the restoring force in newtons. However, this can be automatically converted into other force units via the pull-down menu.

The Math / Science

This equation calculates the approximate value of the restoring force on a pendulum. This equation is derived from equation 13.30. This equation will only work for values when θ is approximately the same as sin(θ), for example 0.1_rad is about the same as sin(0.1)=0.998. Because of this we can substitute in x/L for sin(θ) and come out with approximately the same result.

This formula employs the acceleration due to gravity at sea-level on Earth,(g = 9.80665 m/s²).

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