Investigation of Transient Processes of a Biharmonic Oscillator With a Frequency Multiplicity of 3

The purpose of this study is to investigate transient processes in a biharmonic oscillator featuring two synchronized oscillations at frequencies with a multiplicity of three. As an analytical tool for examining the oscillator's operational modes, we propose a mathematical model in the form of a system of reduced differential equations, derived through transformation of complex impedance expressions describing the elements of the BO equivalent circuit. The solution of the differential equation system for the dynamic operation mode of the biharmonic oscillator is presented graphically through phase portraits for various initial conditions, demonstrating the feasibility of achieving synchronous biharmonic operation. The presented phase portraits, obtained for different ratios of self-excitation margins for each synchronized harmonic of the signal generated by the biharmonic oscillator, illustrate the attainment of stable synchronous biharmonic operation. Additionally, we provide a comparative analysis of transient processes in both presence and absence of active element inertia, implemented in this work through the introduction of a delay line in the oscillator's feedback loop.