Neper frequency, damped harmonic oscillation

[FrankJ777]

Hi all
I'm not sure if this question is better suited for the EE thread or diff eq, but I'm trying to understand what the neper frequency, $$\alpha$$, signifies. I know it's supposed to be the damping factor and that its units are rad/second, but I'm not sure what that implies. It would seem to indicate, by its units, that its rate of oscillation slows by $$\alpha$$ $$rad/second$$, but of course period and frequency remain constant durring damped harmonic oscillation. So can anyone explain to me what I'm missing. In other words if I have a RCL circuit, or a mass and spring system for that matter, what can I predict about the oscillation knowing $$\alpha$$?

Thanks a lot.

 

[Bob S]

A neper is the natural scale of attenuation, and equals 1/e = 0.367879 = -8.686 decibels.
So e^-αt is attenuation of αt nepers.

α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω .