Forced Oscillations

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.

This Demonstration shows the forced oscillations of a spring mass damped system for the underdamped case. The differential equation is , where is the mass, is the displacement, is time, is the damping coefficient, is the stiffness, and is the frequency.

Contributed by: Stephen Wilkerson and Mark Evans (Towson University) (March 2011)
Open content licensed under CC BY-NC-SA



With mass set to 1, adjust the stiffness and the frequency of the forcing function to the maximum to put the system in resonance. Play with dampening to see the effect on the magnitude of the oscillations.

Adjust the stiffness to the maximum and then change the forcing frequency to around 3.4 to observe a beating phenomenon.

Adjust the initial displacement to see the transient response.

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.