Damped Oscillator
A sine wave whose amplitude decays exponentially, centered on a constant level. Use it for damped pendulums, mass–spring systems and ringing electrical circuits.
Parameters
- Amplitude of the decaying envelope at x = 0.
- Decay rate, in inverse units of x. The amplitude falls by a factor of e over a distance 1/b in x.
- Angular frequency, in radians per unit of x. The period is 2π/ω.
- Phase, in radians. Reported between −π and π.
- The constant level the oscillation is centered on.
Tips
- curve.fit does not estimate ω or b automatically, so enter guesses: ω ≈ 2π divided by the period you see, and b ≈ the natural logarithm of the ratio of two successive peak heights (measured from C), divided by the period.
- Include several points per cycle and enough cycles to show the decay.
- A negative Aₒ with δ shifted by π describes the same curve.