Damping in an RLC circuit
To establish the damping calculate ζ (damping ratio). 

\$\zeta = \dfrac{R_{series}}{2}\sqrt{\dfrac{C}{L}}               \$

If ζ is &lt;1 then it is underdamped. If ζ=1 it is critically damped etc.. 

Q (quality factor) is defined as the peak energy stored in the circuit divided by the average energy dissipated in it per cycle at resonance and, Q is \$\dfrac{1}{2\zeta}\$.

You decide what's the best method for you but for me it's easier to use the ζ formula providing you know the values for R, L and C. If you don't know them then there are other methods that involve looking at the step transient response or the frequency response.