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The Crane Operator's Tricks and other Shenanigans with a Pendulum



Stephan Schlamminger, Leon Chao, David B. Newell, Vincent Lee


The dynamics of a swinging payload suspended from a stationary crane can be described as a simple pendulum, typically an unwelcome phenomenon on a construction site. An experienced crane operator can deliver a swinging payload and stop dead on target in a finite amount of time by strictly modulating the speed of the trolley. Generally, a series of precisely timed go-stop movements of the trolley are implemented to damp out the kinetic energy of the simple harmonic oscillator. Here, these mysterious crane operator's tricks will be revealed with a mathematical model, ultimately expanding to a generalized form capturing the case where the load is initially swinging. Finally, this theory is applied to a scientific experiment using a torsion balance to measure $G$, the universal gravitational constant responsible for the swinging of the crane's payload in the first place.
American Journal of Physics


pendulum, control theory, damping, gravitational constant


Schlamminger, S. , Chao, L. , Newell, D. and Lee, V. (2022), The Crane Operator's Tricks and other Shenanigans with a Pendulum, American Journal of Physics, [online],, (Accessed June 14, 2024)


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Created February 18, 2022, Updated November 29, 2022