The simplest amplitude-period formula for non-conservative oscillators

  • Ji-Huan He School of Science, Xi'an University of Architecture and Technology, Xi’an, China
  • Andrés García GIMAP (Grupo de Investigación en Multifísica Aplicada), Universidad Tecnológica Nacional-FRBB, 11 de Abril 461, Bahia Blanca, Buenos Aires, Argentina
Keywords: Periodic orbit, Non-conservative oscillator, Second order ODE.


The simplest frequency formulation for conservative oscillators was proposed in 2019 (Results Phys 2019;15:102546). However, it becomes invalid for non-conservative oscillators. This work suggests the simplest amplitude-period formulation for non-conservative oscillators. The existence of a periodic solution of a second-order ordinary differential equation is given, and the periodic orbits are easily obtained. To the best of the authors’ knowledge, such a powerful result is not available in the literature, providing a tool to determining periodic orbits/limit cycles in the most general scenario.


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How to Cite
He , J.-H., & García , A. (2021). The simplest amplitude-period formula for non-conservative oscillators. Reports in Mechanical Engineering, 2(1), 143-148.