Solving for Bode Critical Frequency: Guide and Equation Explanation

[fractal01]

I am given a bode plot and have to label the cutoff frequency on there.
G(jw)=2/(-w^2 +162jw +320)

I got this equation where w is the critical frequency:
70922=81^2 + (170 -(w^2/4))

I am sure that this is wrong since I get the sqrt of a negative number for w.

It would be really great if someone could help!

 

[gneill]

-ω² is equivalent to (jω)². So let s = jω and your transfer function becomes:
$$\frac{2}{s^2 + 162s + 320}$$
The denominator has a pair of negative valued roots which should correspond to (angular) frequencies of interest.