Charge. Ring. Follow the energy.
An ideal series RLC circuit. Connect electrical damping and resonance to the mechanical system you already know.
One voltage, different ringing
Does adding resistance change the final capacitor voltage or the way it gets there?
Pin R = 1 Ω for a 5 V step. Change only R to 8 Ω (critical), then 10 Ω. Compare capacitor voltage and current; keep L, C and initial conditions fixed.
Synchronized signals
Select a trace or use the replay slider. The first current signal is cyan; secondary signals and numbered pinned runs are dashed. Every setting change recalculates from the initial state.
Compare one change 0/3
Keep initial state, inputs and seed matched when comparing controllers. Pinned traces retain their original settings and stop time.
Observed result
Recorded duration: 0 s · Clipped command time: — s
Energy balance residual: J
These observations describe a finite run, not a general stability or robustness guarantee.
Equations, assumptions and method
C vC′ = i; L i′ = vin − Ri − vC; E = ½C vC² + ½L i²
Ideal voltage source, linear resistor, inductor and capacitor. There is no feedback controller, source current limit, parasitic resistance or breakdown model. RK4 at 1 ms integrates both states, source work and resistor loss; samples every 20 ms. E(t) − E(0) = source work − resistor loss. Large resonance voltages are mathematical predictions within these assumptions, not equipment ratings. A finite trace may still include startup transients.