The motion of a Swinging Atwood Machine is a difficult to solve for using Newtonian Mechanics. Lagrangian Mechanics, on the other hand, is extremely useful tool for a system that can seem overwhelmingly difficult to solve in Newtonian Mechanics. In this Lab we find the Lagrangian for this Swinging Atwood system, solve for the equation of motion, and compare our model to that of the observed motion of the system. Our model provides a good approximation of the motion, with small discrepancies due to the unknown mass of our pulley and dissipative forces.
Moody, Parker W.
"Modeling a Swinging Atwood Machine,"
The Journal of Advanced Undergraduate Physics Laboratory Investigations, JAUPLI-B: Vol. 2, Article 1.
Available at: https://digitalshowcase.lynchburg.edu/jaupli-b/vol2/iss1/1