We have experimentally demonstrated dissipative coupling in a double pendulum system through observation, which shows three distinctly different patterns of motion over the accessible parameter space. The described dissipative coupling apparatus is easy to manufacture and budget-friendly. The theoretical calculations are also suitable for the undergraduate level. Our experiment can serve as a novel demonstration for ubiquitous dynamic coupling effects encountered in many disparate physical systems. Unlike the well-known spring-coupled pendulums, our experiment employs Lenz's effect to couple the pendulums through electromagnetic damping, which, to the best of our knowledge, has not been demonstrated in the classroom. Our pendulums exhibit level attraction behaviour between two modes, induced by the dissipative coupling. This stands in contrast to the traditionally taught concept of level repulsion (avoided crossing) with spring-coupled pendulums. This experiment showcases distinctly different time domain dynamics of the dissipatively coupled pendulums over the parameter space, characterized by different oscillation patterns, damping rates, and relative phase between the two pendulums, which is a valuable lesson elucidating the dynamics of synchronization in linear systems for undergraduate students.
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An experimental demonstration of level attraction with coupled pendulums
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August 2023
August 01 2023
An experimental demonstration of level attraction with coupled pendulums
Chenyang Lu;
Chenyang Lu
a)
Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba
, Canada
R3T 2N2
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Bentley Turner;
Bentley Turner
b)
Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba
, Canada
R3T 2N2
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Yongsheng Gui;
Yongsheng Gui
c)
Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba
, Canada
R3T 2N2
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Jacob Burgess;
Jacob Burgess
d)
Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba
, Canada
R3T 2N2
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Jiang Xiao;
Jiang Xiao
e)
Department of Physics and State Key Laboratory of Surface Physics, Fudan University
, Shanghai 200433, China
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Can-Ming Hu
Can-Ming Hu
f)
Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba
, Canada
R3T 2N2
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Am. J. Phys. 91, 585–594 (2023)
Article history
Received:
December 10 2021
Accepted:
June 19 2023
Citation
Chenyang Lu, Bentley Turner, Yongsheng Gui, Jacob Burgess, Jiang Xiao, Can-Ming Hu; An experimental demonstration of level attraction with coupled pendulums. Am. J. Phys. 1 August 2023; 91 (8): 585–594. https://doi.org/10.1119/5.0081906
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