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Two Coupled Oscillators

  • Leonid I. ManevitchEmail author
  • Agnessa Kovaleva
  • Valeri Smirnov
  • Yuli Starosvetsky
Chapter
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)

Abstract

Let us consider first the most simple nonlinear problem of energy transfer in the system of two weakly coupled nonlinear oscillators with cubic restoring forces (Fig. 1.1). Its linearized version is a widely used example of beating phenomenon. In this limiting case, due to superposition principle, every vibrational process can be presented as a combination of two basic oscillations corresponding to in-phase and out-of-phase linear normal modes. If the coupling between the oscillators is relatively weak and only one of oscillators is initially excited, the beat with a slow periodic inter-particle energy exchange is observed.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Leonid I. Manevitch
    • 1
    Email author
  • Agnessa Kovaleva
    • 2
  • Valeri Smirnov
    • 1
  • Yuli Starosvetsky
    • 3
  1. 1.Institute of Chemical PhysicsRussian Academy of ScienceMoscowRussia
  2. 2.Space Research InstituteRussian Academy of ScienceMoscowRussia
  3. 3.Technion—Israel Institute of TechnologyFaculty of Mechanical EngineeringHaifaIsrael

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