Free Vibrations of a Spring-Mass-Damper System

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The derivation here follows the usual form given in [1], in which , , and are the mass, damping coefficient, and spring stiffness, respectively. The variable in this system is . Applying Newton's second law gives the differential equation , where and .

Contributed by: Stephen Wilkerson (Army Research Laboratory and Towson University), Nathan Slegers (University of Alabama Huntsville), and Chris Arney (United States Military Academy, West Point) (March 2011)
Open content licensed under CC BY-NC-SA




[1] S. Timoshenko, D. Young, and W. Weaver Jr., Vibration Problems in Engineering, 4th ed., New York: John Wiley & Sons, 1990.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.