I am unable to relate the Barkhausen criterion for oscillations to sustain to the Ideal LC oscillator with an initial condition. Assume you have a parallel combination of LC(both with Q=infinity) with an initial condition say V volts on capacitor. Mathematically it will oscillate with the frequency 1/2/pi/sqrt(LC). Now I see no feedback here. where you apply barkhausen criterion for the oscillations in that feedback system? Even if there is a loss in inductor and I keep a -ve resistance in parallel to cancel out that loss, how can i apply the Barkhausen criterion for this as well.