The transfer function of a second order system (e.g., RCL circuit with
voltage across the capacitor C) as the output) is

where is an arbitrary gain factor. If we let , we get the frequency transfer function

Specially, when , we have

with magnitude

The Bode plot of this transfer function can be found as

and

To obtain the asymptotic approximation of this function, consider the following three cases:

- When
i.e.,
, we have

and

- When
, we have

and

- When
, we have

and

We see that the smaller , the larger , and the sharper and narrower the peak.