Varying Period of a Damped Pendulum

This Demonstration explores the effect that the rod length, damping coefficient, and initial position have on the period of a damped pendulum.
Mathematica's built-in function WhenEvent, triggered whenever the bob crosses the vertical, detects the time of successive swings of the pendulum.
The actual swing period can be compared to the theoretical one that is valid for small initial angles only, , where is time and is the acceleration due to gravity.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The well-known equation of motion of the damped pendulum is used: , where is the angle from the vertical, is time, is the acceleration due to gravity, is the length of the pendulum, and is the damping factor.
During the solution of the differential equation, WhenEvent is triggered by the event and the resulting action collects the time at each crossing.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+