Motion of a Swinging Atwood’s Machine: Simulation and Analysis with Mathematica

Abstract

A generalized model of the Atwood machine when one body is constrained to move along a vertical axis while the other one can swing in a plane is considered. Combining symbolic and numerical calculations, we have obtained equations of motion of the system and analyzed their solutions. We have shown that oscillation can completely modify a motion of the system while the simple Atwood machine demonstrates only the uniformly accelerated motion of the bodies. The validity of the results obtained is demonstrated by means of the simulation of motion of swinging Atwood’s machine with the computer algebra system Wolfram Mathematica.