Driven Oscillator Amplitude
The displacement amplitude of a driven, damped oscillator against driving frequency: a resonance peak on a constant baseline. Use it for a mechanical oscillator’s amplitude or the capacitor voltage of a driven series RLC circuit.
Fit the example dataStart with your own data
Example: simulated amplitude of a driven mass on a spring, 36 points with x and y uncertainties, opened as a new copy you can edit.
Parameters
- Scale factor. With light damping, the peak height above C is about A/(2βωₒ).
- Natural (undamped) angular frequency, in the units of x.
- Damping constant, in the units of x. Reported as positive unless a requested limit requires the negative equivalent.
- Constant baseline.
Tips
- This model was called Lorentzian before 2.13. It is not the Lorentzian line shape of spectroscopy; for that, use Lorentzian Peak.
- For the current in a series RLC circuit, or the voltage across its resistor, use RLC Resonance. That response has a different shape: fitting it with this model makes ωₒ about 5% too high at Q = 3, and 1% at Q = 10, with Q further off.
- The peak lies at x = √(ωₒ² − 2β²), a little below ωₒ. With light damping, the height above C falls to 1/√2 of its peak value about β either side of the peak, so the quality factor is about ωₒ/(2β).
- Use the same units for x, ωₒ and β. If the fit does not converge, enter guesses: ωₒ near the peak position and β near half the width of the peak at 1/√2 of its height.