Oscillations of a Mass-Spring System on an Inclined Plane
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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.