Quantum mechanics

Differential equation

Periodic function

Limit (mathematics)

Acoustics

Classical mechanics

Dentistry

Physics

Calculus (dental)

Amplitude

Mathematics

Work (physics)

Mathematical analysis

Ordinary differential equation

Medicine

Periodic orbits

Period (music)

Reports in Mechanical Engineering

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.

The simplest amplitude-period formula for non-conservative oscillators