Lorentzian
The amplitude of a driven, damped oscillator against driving frequency: a resonance peak on a constant baseline. Use it for resonance curves of mechanical oscillators and AC circuits.
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 is the resonance form, not the Lorentzian line shape A/((x − x₀)² + γ²) of spectroscopy. For that shape, use a Custom Function such as
A/((x-B)^2+C^2)+D. - 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: all angular frequencies, or all in hertz.
- 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.