I don't want to discourage any experimentations, but I looked at the paper smuge posted, about the negative resistance, and I would say it's a bit more complex than that, since coils have inter winding capacitance, resistance, etc.
However, the math deriving the negative resistance does look right assuming a phase "delay" in the mutual coupling of ideal inductors. But that's the big IF, is there really a phase shift? Yes there is always propagation delay, between objects spaced apart, since energy travels with the speed of light, but does that produce extra energy? No I don't believe so.
So what's the problem?
Well it appears at face value to be a case of mixing apples with oranges, i.e. Mixing time domain analysis with sinusoidal steady state analysis. Talking about a phase shift implies steady state, meaning the transients have died down, and we're exciting the circuit with a pure sinusoidal signal.
EM
