Theoretical analysis of the swinging Atwood's machine with pendulum-in-pendulum system

Abstract

The swinging Atwood's machine, whose motion was initially explored by Tufillaro et al. [Am. J. Phys. 52, 895 (1984)], is a twist on Atwood's machine where one mass is able to move freely across the plane and swing about its pulley as long as the string is always taut. In this paper, we add a twist to this same system by replacing the swinging mass with a pendulum-in-pendulum system and explore its resulting motion. The system's equation of motion was first obtained, then through numerical integration, simulated to observe its motion.