Oscillations of a Mass-Spring System on an Inclined Plane

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 oscillations of a system composed of two identical springs with force constant attached to a disk of radius and mass that rolls without sliding on a plane inclined at angle . The resultant amplitude is .

Contributed by: Edwin Loaiza Acuña (March 2011)
(Universidad del Valle sede Buga. Guadalajara de Buga, Colombia, Sudamérica)
Open content licensed under CC BY-NC-SA



Using Newton's second law, it is possible to establish the equilibrium point , where is the length of the incline, is the acceleration due to gravity, and is a parameter that determines the rotation of the wheel. By energy conservation, one can find the angular frequency: . From this, the equation of motion for the coordinate, measured along the surface, is found to be . The parameters , , , , and all appear in the result.

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.