Linear Stability Analysis of Harmonic Oscillator in The Domain of Super Conductivity

Abstract

Harmonic oscillator or tank circuit is an idealized model because there is no dissipation of energy due to resistance. Tank circuit is used for creating signals at a certain frequency from a compound signal. In RLC circuit the resistor in series will start throwing away the power that should go to the load and due to unwanted resonance it would affect the stability of the system and it creates audible noise in RF circuits. In order to encounter this situation an LC circuit is used and this circuit will not waste that power. The technique used for analyzing the behavior mathematically and graphically is linear stability analysis. Linear stability analysis tells us about the behavior of a system near an equilibrium point. Linear stability analysis of harmonic oscillator in the domain of superconductivity determines the stability of fixed points in a circuit to visualize the qualitative analysis of resonance frequency when an LC circuit is operated from an external supply.