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For Students · Oscillator Designer

Oscillator Designer for a resonant circuit

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a resonant circuit live below — adjust the inputs and watch it respond, right in your browser.

RLC Circuit

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RLC Circuit StudioLive

series RLC step response

Controls

Apply a step voltage to a series RLC circuit and watch charge and current respond — under-, over-, or critically damped.

Presets

Resistance R

Inductance L

Capacitance C

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Data Inspector

Damping ζ0.750

Regimeunderdamped

ω₀1.000

Governing equation

1 \overset{q}{¨} + 1.5 \overset{q}{˙} + \frac{q}{1} = V_{0}, ω_{0} = \frac{1}{L C} = 1.000, ζ = \frac{R}{2} \frac{C}{L} = 0.750

Reading this result: ζ = 0.750 < 1: underdamped. With ω₀ = 1.000 rad/s the charge overshoots and rings, oscillating while it decays toward its steady value. Lower ζ means more ringing.

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Bode Plot

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Bode Plot (2nd-Order System)Live

frequency response

Controls

Presets

Natural frequency (Hz)

Damping ratio ζ

A Bode plot shows how a system responds across frequency: gain in decibels on top, phase shift below. This second-order low-pass passes low frequencies and rolls off at −40 dB/decade above its natural frequency. Low damping produces a resonant peak; high damping smooths it away.

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Data Inspector

Natural freq1,000 Hz

Damping ζ0.30

Resonant peak+4.8 dB

Roll-off−40 dB/dec

Governing equation

H (s) = \frac{ω _{n}^{2}}{s ^{2} + 2 ζ ω _{n} s + ω _{n}^{2}} = \frac{6 , 28 3 ^{2}}{s ^{2} + 3770 s + 6 , 28 3 ^{2}}

Reading this result: Low damping ζ=0.30 produces a sharp +4.8 dB resonant peak just below fn — great for selectivity, but it rings in the time domain.

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Frequently asked questions

Is this good for students?: Yes — this version of "Oscillator Designer for a resonant circuit" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.