I have a doubt regarding the angular frequency of a harmonic oscillator when there is damping involved. The frequency of the oscillation changes with time in the case of damping, but I haven't seen mention of this anywhere. I would like to find how the angular frequency depends on time (I'm guessing there must be some function $\omega=\omega(\omega_0,t,\beta)$ or something like that, where $\beta$ refers to the damping coefficient and the $\omega$'s refer to frequencies).
I checked with Landau and Taylor; neither of them, as far as I can see, discuss this phenomenon (although of course they talk about the decrease in amplitude and all that).
I'm pretty sure this phenomenon of frequency decreasing with time does occur (I checked quickly with a mish-mash harmonic oscillator), so why doesn't anyone mention it?
Could someone explain to me the time dependence of frequency when there are damped oscillations? Or maybe point out resources I could check out that do talk about this?