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
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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.
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