Abstract
With the development of chaos theory, Duffing oscillator has been extensively studied in many fields, especially in electronic signal processing. As a nonlinear oscillator, Duffing oscillator is more complicated in terms of equations or circuit analysis. In order to facilitate the analysis of its characteristics, the study analyzes the circuit from the perspective of vibrational science and energetics. The classic Holmes-Duffing model is first modified to make it more popular and concise, and then the model feasibility is confirmed by a series of rigorous derivations. According to experiments, the influence of driving force amplitude, frequency, and initial value on the system is finally explained by the basic theories of physics. Through this work, people can understand the mechanisms and characteristics of Duffing oscillator more intuitively and comprehensively. It provides a new idea for the study of Duffing oscillators and more.
Highlights
Chaos theory was first proposed by Lorentz, who found the butterfly effect in the simulation of Earth meteorology
This study studies the Duffing oscillator from the perspective of mechanics
The results show that the input energy is the decisive factor that determines the final state of the oscillator, which is determined by the external driving force Fd
Summary
Chaos theory was first proposed by Lorentz, who found the butterfly effect in the simulation of Earth meteorology. Holmes simplified the parameter and obtained Duffing-Holmes oscillator with complex chaotic behavior.[3] He made a corresponding physical model and confirmed its characteristics. People use this oscillator to detect weak signals.[4,5,6]. The forces that affect the oscillator motion is the spring force, the Coulomb force between charges, the damping force, and the electric field force exerted on the oscillator by a uniform electric field They are independent to each other and analyzed, respectively. Since the three charges are in a straight line, the Coulomb resultant force of the oscillator is affected by two negative charges
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