Units of damping terms for harmonic oscillator I understand that in the equation of motion of a simple harmonic oscillator $\ddot{x} + \omega_0^2 x = 0$, $\omega_0$ has dimension inverse time.  Since solutions are of the form $x(t) = A \cos (\omega_0 t + \phi)$, I also understand that $\omega_0$ is an angular frequency, and is often expressed in units of rad/s.
Now if we add a viscous damping term, the equation of motion can be written as $\ddot{x} + \gamma \dot{x} + \omega_0^2 x = 0$.  The dimensions of $\gamma$ are again an inverse time, but I am confused about its units, in other words is it a frequency or an angular frequency?
I know for instance that the solutions will be proportional to $e^{-\gamma t/2}$, and that makes me think the units of $\gamma$ are /s, but I am not sure.  On the other hand, the quality factor is $\omega_0/ \gamma$.
In practice, if I apply this to a series RLC circuit, $\gamma = R/L$ is an inverse time, but for $R$ in Ohms, and $L$ in Henries, do we get /s or rad/s?
 A: $\gamma$ is not a frequency or an angular frequency (although it has the same units, 1/s). Think of $1/\gamma$ as relaxation time.
As concerns the second part of your question, just look up Henries and Ohms in SI units and work your way from there on.
Edit (after @Mister Mak's comment): To clarify the difference between frequency and angular frequency, between rad/s and 1/s.
Rad is of course dimensionless and not that much of a physical dimension. Well, it is, as I just learnt from Wikipedia^^, but $1\,$rad $= 1$, you know... It's just giving you context to say that angles are involved somehow.
A pendulum oscillating with a frequency $f$ reaches the same state after a time $T=1/f$. Describing its trajectory with a sine you have
$$
x\left(t\right) = \sin\left(2 \pi f t\right)
$$
wherein it may be convenient to use the angular frequency $\omega = 2 \pi f$, just as a shorter notation.
As concerns $\gamma$ in your example of a damped pendulum, it is not used in a sine, not describing an oscillation or a periodic process, so there is no point in measuring it in rad/s. I mean, you could, but that would be pointless, a bit like selling $4\,$rad eggs.
A: Radian really has no unit, it is something related to notation. As radians refer to the arclength divided by the full perimeter of a circumference, it has no units. Therefore, it doesn't matter as frequency $f$ is $2\pi w$, so both have the same units ($s^{-1}$).
