Oscillations of a Mass-Spring System on an Inclined Plane

time t

0

angle α

30

amplitude A

0.25

force constant K

5

mass M

5

This Demonstration shows the oscillations of a system composed of two identical springs with force constant

K

attached to a disk of radius

R

and mass

M

that rolls without sliding on a plane inclined at angle

α

. The resultant amplitude is

A

.

Details

Using Newton's second law, it is possible to establish the equilibrium point

x

0

=

1

2

L-

MgRsinθ

K

, where

L

is the length of the incline,

g

is the acceleration due to gravity, and

θ

is a parameter that determines the rotation of the wheel. By energy conservation, one can find the angular frequency:

2

ω

=

4K

3M

. From this, the equation of motion for the

x

coordinate, measured along the surface, is found to be

x(t)=

x

0

+Acos(ωt)

. The parameters

θ

,

L

,

M

,

K

, and

A

all appear in the result.

Permanent Citation

Edwin Loaiza Acuña

"Oscillations of a Mass-Spring System on an Inclined Plane"
http://demonstrations.wolfram.com/OscillationsOfAMassSpringSystemOnAnInclinedPlane/
Wolfram Demonstrations Project
Published: December 6, 2010