10981

# 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.

### DETAILS

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.

### PERMANENT CITATION

 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 » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.