Characteristics from transfer function
The standard form for a two-pole low-pass filter is:

$$\frac{K\,\omega_{_0}^2}{s^2+2\,\zeta\,\omega_{_0}\,s+\omega_{_0}^2}$$

\$K\$ is the gain. \$\zeta\$ is the damping factor (with \$Q=\frac{1}{2\,\zeta}\$, being the ratio of the center frequency to the \$-3\:\text{dB}\$ frequency.)

If the denominator is expressed as \$b_2\,s^2+b_1\,s+b_0\$, then \$\omega_{_0}=\sqrt{\frac{b_0}{b_2}}\$ and \$\zeta=\frac{b_1}{2\,\sqrt{b_0\,b_2}}\$. (You may also want to consider what the value of \$K\$ must be, too.)

If you are interested in more detail, I've provided it here.