Resonant WPT Circuit: Exact Normal-Mode Splitting

This is the circuit-level counterpart to the flagship 3D coupled-mode-theory simulator: instead of the narrowband slowly-varying-envelope approximation, it integrates the exact two-loop mutual-inductance RLC circuit equations live with an RK4 solver, and solves the same equations' steady-state response in closed form via impedance algebra. Two schematic resonant loops are drawn with an animated instantaneous current readout, a scrolling oscilloscope trace of their amplitude envelopes, and a transfer-efficiency spectrum built from the exact circuit response. Push the coupling coefficient k past the critical value k_c = 1/Q with the drive parked at ω₀ and watch the single resonance bifurcate into two peaks at the exact undamped normal-mode frequencies ω± = ω₀/√(1∓k) — while the oscilloscope shows the two loops' currents visibly beating against each other, the time-domain signature of the same frequency-splitting phenomenon that real strongly-coupled magnetic-resonance WPT systems must track or avoid.