Swinging Atwood's Machine

t

100.

6.5

6.5

r

0

1.67

θ

0

1.82

r'(0)

0.68

θ'(0)

-0.63

This Demonstration solves a system of two masses hanging from two pulleys, with one of them swinging and the other moving vertically, a system known as a "swinging Atwood's machine." The variables of the system are the angle

θ

and

r

, the length of the string of the swinging mass, both depending on the time

t

. Friction is neglected.

Details

The equations of motion are

..

r

=

r

2



θ

+g(cosθ-μ)

1+μ

,

..

θ

=-

2



r



θ

+gsinθ

r

,

where

g

is the gravitational acceleration.

References

[1] D. Morin, Introduction to Classical Mechanics with Problems and Solutions, New York: Cambridge University Press, 2008 pp. 15.

[2] Wikipedia. "Swinging Atwood's Machine." (Nov 26, 2012) en.wikipedia.org/wiki/Swinging_Atwood%27s_machine.

[3] D. Lu. Trajectories of the Swinging Atwood's Machine.[Video] (Apr 24, 2011) www.youtube.com/watch?v=oVsfdM9sacI.

External Links

Gravitational Acceleration (ScienceWorld)

Pulley (ScienceWorld)

Permanent Citation

Enrique Zeleny

"Swinging Atwood's Machine"
http://demonstrations.wolfram.com/SwingingAtwoodsMachine/
Wolfram Demonstrations Project
Published: March 13, 2013