Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 31, 07 March 2024
Open
Access | Article
Metronome synchronization in the presence of friction
* Author to whom correspondence should be addressed.
Abstract
This study investigates the synchronization phenomenon inherent to mechanical metronomes. Synchronization properties were probed under diverse conditions, with modifications to parameters such as the number of metronomes, the tabletop material, the additional weight on the platform, and the friction coefficient between the roller and platform. Experimental outcomes demonstrate that the synchronization is significantly influenced by the platform's movement, which is subsequently determined by the properties of both the platform and roller. An analytical modeling approach provided insights into these effects, particularly when analyzing two metronomes placed on a flat platform equipped with rollers. Central to the findings is the revelation that both the coefficient of friction and the mass of supplementary weights play crucial roles in shaping synchronization behavior, a conclusion in line with experimental observations. The numerical segment of the study leveraged the Kuramoto model. Observations centered on the phase variation of resonators and a time-responsive order parameter, shedding light on the role of coupling strength in synchronization and its absence. Overall, this study furnishes a thorough theoretical and experimental exploration of mechanical metronome synchronization, targeting an enhanced understanding and application of the observed phenomenon.
Keywords
metronomes, frictional force, synchronization, numerical modeling
References
1. Tajima H, Funo K, Superconducting-like Heat Current: Effective Cancellation of Current-Dissipation Trade-Off by Quantum Coherence[J], Physical Review Letters, 2021, 127(19): 190604.
2. Ticos C, Rosa E, Pardo W, et al., Experimental real-time phase synchronization of a paced chaotic plasma discharge[J], Physical Review Letters, 2000, 85(14): 2929.
3. Ramirez J, Nijmeijer H, The secret of the synchronized pendulums[J], Physics World, 2020, 33(1): 36.
4. Buck J, Buck E, Mechanism of Rhythmic Synchronous Flashing of Fireflies: Fireflies of Southeast Asia may use anticipatory time-measuring in synchronizing their flashing[J], Science, 1968, 159(3821): 1319-1327.
5. Rayleigh J W S B. The theory of sound[M]. Macmillan, 1896.
6. Huygens Ch, Œuvres complètes[M], Swets & Zeitlinger B. V., Amsterdam, 1967.
7. Bennett M, Schatz M F, Rockwood H, et al. Huygens's clocks[J]. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2002, 458(2019): 563-579.
8. Pantaleone J. Synchronization of metronomes[J]. American Journal of Physics, 2002, 70(10): 992-1000.
9. Kuznetsov N V, Leonov G A, Nijmeijer H, et al. Synchronization of two metronomes[C]//PSYCO. 2007: 49-52.
10. Hutchings I, Shipway P. Tribology: friction and wear of engineering materials[M]. Butterworth-heinemann, 2017.
11. Cartwright J H E, Piro O. The dynamics of Runge–Kutta methods[J]. International Journal of Bifurcation and Chaos, 1992, 2(03): 427-449.
12. Acebrón J A, Bonilla L L, Vicente C J P, et al. The Kuramoto model: A simple paradigm for synchronization phenomena[J]. Reviews of modern physics, 2005, 77(1): 137.
Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Authors who publish this series agree to the following terms:
1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this series.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this series.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See Open Access Instruction).
- Volume Title
- Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
- ISBN (Print)
- 978-1-83558-317-3
- ISBN (Online)
- 978-1-83558-318-0
- Published Date
- 07 March 2024
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/31/20240888
- Copyright
- 07 March 2024
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited