Dummy to dummy sine wave oscillator theory

A sine wave oscillator is a circuit able to produce a signal shaped as a sinewawe with a stable amplitude and frequency. The basic idea is to leverage how an inductance and a capacitor swaps alternatively their energy providing some strategy to mantain this exchange always running. Lets see an example circuit:

The inductor has a series resistence of 1Ohm. The generator produce a pulse, and now we look at the simulation on the falling edge of that pulse, we analyze the voltage on L1.

















as we can see before reaching 0 the voltage jump around the 0 some times, we can imagine without be too far from the reality that the energy contained in the inductor as a magnetic field will pump current in the capacitor that store that energy as an electric field. The Process repeats util the energy dissipate as heat.
There is a demostrable equation giving us the frequency at which this exchange happens,  showing that frequency influenced just by capacitor and inductor. Parasitic resistance does not change the frequency but the signal damping. This formula is:

Well let's try to play with the circuit simulator, what would happen if the inductor has a series resistance with a negative value? By picking a not so randomly value of -460Ohm:

As you can see, the oscillator is stable, and produce a continuos sinewawe signal. Unfortunately we can't buy a negative resistance, but there is active component that can emulate, per se or in a certain circuit, a negative resistance, and this is the basis to create this kind of oscillator.