Analysis of Synchronization of Mechanical Metronomes

  • Tohru IkeguchiEmail author
  • Yutaka Shimada
Conference paper
Part of the Understanding Complex Systems book series (UCS)


Synchronization phenomena are ubiquitous around us and are observed in various real systems, for example, hands clapping (rhythmic applause) at the concert hall, light emission of fireflies, callings of frogs, circadian rhythms, pendulum clocks, mechanical metronomes placed on a plate, pedestrians on a suspension bridge, water flowing out of plastic bottles connected by hoses, candle flames fluctuation. In this paper, we focused on the synchronization phenomena observed in a mechanical system: mechanical metronomes on a plate. In particular, we discussed how to construct a mathematical model, or the equations of motion, which describe dynamical behavior of synchronization of mechanical metronomes put on a plate hung by strings. We also investigated their dynamical behavior by solving the equations of motions numerically. In the numerical experiments, parameter values of the equations of motion are experimentally obtained from the experimental equipment. We found that synchronization behavior of mechanical metronomes depends on the following two factors: relation between the frequencies of the metronomes and the plate, and initial angles of the metronomes. We also found the individual difference of the metronomes strongly affects the final behavior. In addition, the results also indicate that if the number of mechanical metronomes increases, it becomes extremely harder to observe the in-phase synchronization until energy applied to the metronomes through spiral springs is exhausted.


  1. 1.
    A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Science, Cambridge Nonlinear Science Series (Cambridge University Press, Cambridge, 2003)CrossRefGoogle Scholar
  2. 2.
    F.E. Hanson, J.F. Case, E. Buck, J. Buck, Synchrony and flash entrainment in a new guinea firefly. Science 174, 161–164 (1971)CrossRefGoogle Scholar
  3. 3.
    I. Aihara, T. Mizumoto, T. Otsuka, H. Awano, K. Nagira, H.G. Okuno, K. Aihara, Spatio-temporal dynamics in collective frog choruses examined by mathematical modeling and field observations. Sci. Rep. 4(3891) (2014)Google Scholar
  4. 4.
    Ikeguchi Laboratory, Synchnonization of 32 metronomes (2014), YouTube
  5. 5.
    Ikeguchi Laboratory, Synchnonization of 100 metronomes (2015), YouTube
  6. 6.
    Y. Sato, K. Nagamoto, T. Nagamine, M. Fuse, Synchronized phenomena of oscillators (experimental and analytical investigation for two metronomes). Trans. Jpn. Soc. Mech. Eng. 66(642), 9–15 (2000)Google Scholar
  7. 7.
    J. Pantaleone, Synchronization of metronomes. Am. J. Phys. 70(10), 992–1000 (2002)CrossRefGoogle Scholar
  8. 8.
    Y. Fujino, B.M. Pacheco, P. Warnitchai, S.I. Nakamura, Synchronization of human walking observed during lateral vibration of a congested pedstrian bridge. Earthq. Eng. Struct. Dyn. 22(9), 741–758 (1993)CrossRefGoogle Scholar
  9. 9.
    S.H. Strogatz, D.M. Abrams, A. McRobie, B. Eckhardt, E. Ott, Crowd synchrony on the milleninium bridge. Nature 438, 43–44 (2005)CrossRefGoogle Scholar
  10. 10.
    Ikeguchi Laboratory, Synchnonization of petbottle oscillators (in-phase) (2010), YouTube
  11. 11.
    Ikeguchi Laboratory, Synchnonization of petbottle oscillators (out-of-phase) (2010), YouTube
  12. 12.
    H. Kitahata, J. Taguchi, M. Nagayama, T. Sakurai, Y. Ikura, A. Osa, Y. Sumino, M. Tanaka, E. Yokoyama, H. Miike, Oscillation and synchronization in the combustion of candles. J. Phys. Chem. A 113(29), 8164–8168 (2009)CrossRefGoogle Scholar
  13. 13.
    Ikeguchi Laboratory, Synchnonization of candle oscillators (2009), YouTube
  14. 14.
    S. Nakata, T. Miyata, N. Ojima, K. Yoshikawa, Self-synchronization in coupled salt-water oscillators. Phys. D Nonlinear Phenom. 115(3–4), 313–320 (1998)CrossRefGoogle Scholar
  15. 15.
    Ikeguchi Laboratory, Synchnonization of salt-water oscillators (2011), YouTube

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Information and Computer TechnologyTokyo University of ScienceTokyoJapan
  2. 2.Department of Information and Computer SciencesSaitama UniversitySaitamaJapan

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