Turn the knobs and watch the transient like an oscilloscope. Freeze a trace, then tweak one knob to compare.
This demo uses the series RLC driven by a voltage step. The “knobs” change the physics directly: R dissipates energy, while L and C store energy and exchange it back and forth.
The page is meant to make transient behavior feel concrete: how ringing emerges, how damping removes it, and how initial energy can reshape the waveform even when the external input looks simple.
The waveform is not controlled by just one idea. It is shaped by energy storage, energy loss, and the initial conditions. That is why the same step input can produce ringing, fastest no-overshoot settling, or a slow heavy return depending on where the circuit sits in damping space.
Start from a known regime, then tweak one knob at a time. Freeze a previous trace, then compare how the new transient changes. Use energy overlays when you want to see where the “motion” of the waveform is really coming from.
The original interactive prototype is preserved below. You can adjust the physical knobs, apply presets, switch between capacitor voltage and series current, and compare traces directly.
Tip: set R low to see ringing. Click Freeze & Compare, then increase R to watch damping.
This demo uses the series RLC driven by a voltage step. The “knobs” change the physics directly: R dissipates energy, while L and C store energy and exchange it back and forth.
We simulate two state variables: series current i(t) and capacitor voltage vC(t). For a source vs(t) (step), KVL gives:
Combine them into two first-order ODEs:
The page integrates these equations with a lightweight RK4 solver (fast enough to update while you drag sliders).
Two simple quantities predict the waveform shape:
Interpretation: ω0 gets smaller if you increase L or C → oscillations slow down. ζ increases with R → ringing dies out faster.
For a series RLC, the critical resistance is:
In a lossless LC, energy would “sloshe” forever between electric and magnetic storage. Adding R converts some of that energy into heat.
Try this: make R small (ringing), turn Energy: On, then increase R. You’ll see the same energy exchange, but the loss grows faster and the oscillation fades sooner.
Set step amplitude to a small value (e.g., 0.5 V), then inject energy using Vc0 or I0. You’ll get very different transients even with the same R, L, C — because transients are about initial energy as much as input waveforms.