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Resonances and Periodic Motions of Atwood’s Machine with Two Oscillating Weights

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Abstract

The problem of constructing periodic solutions to the equations of motion of Atwood’s machine in which both weights have the same mass and can oscillate in the vertical plane is discussed. Differential equations governing the motion of this system are derived, and an algorithm for calculating their solutions that determine periodic oscillations of the weights under the condition that the oscillation frequencies are in resonance \(n{{\omega }_{1}} = m{{\omega }_{2}}\), where n and m are natural numbers, is proposed. These solutions are obtained in the form of series in a small parameter. The comparison of the results with numerical solutions of the equations of motion confirm the validity of the obtained solutions. All computations are performed using the computer algebra system Wolfram Mathematica.

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  1. Warsaw University of Life Sciences, 02-776, Warsaw, Poland

    A. N. Prokopenya

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  1. A. N. Prokopenya
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Correspondence to A. N. Prokopenya.

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Translated by A. Klimontovich

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Prokopenya, A.N. Resonances and Periodic Motions of Atwood’s Machine with Two Oscillating Weights. Program Comput Soft 49, 433–440 (2023). https://doi.org/10.1134/S0361768823020135

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