Damped wave expression

[John77]

Hi everybody!

The last expression was derived by converting an underdamped harmonic oscillation to a travelling wave. Actually, I searched everywhere and I did not find such expression (it can be also wrong).

The loss factor (l) and the wave number (λd) are replaced by an expression depended by the damped frequency. Although in most applications the damped frequency is calculated and not used as input (as the loss factor) to the expression, could the last expression be a valid solution for the underdamped wave equation when the initial frequency (ω0) is known? Or is the wavenumber correct for the damped wave expression?

 

Edited June 29, 2019 by John77