NOTE: Later there may be more discussion here, but for now this is just an example of getting the frequency response from a transfer function.

Assume you are given the transfer function:

that relates two variables of interest.  Recall, a transfer function is a ratio of one variable to another, typically, and this could be the output variable of interest over the input variable.

To get the frequency response, or amplitude and phase functions, first identify that because s = jw, this is a complex function (j is complex operator).  Simply substitute jw for s.

The amplitude and phase functions refer to the polar form of this complex function.  Recall, a complex number z = a + jb can be written as z = r exp (j g), where r is the absolute value of z and g is the argument of z, and j is the square root of -1.

In the transfer function above, you need to use some of the basic rules for complex numbers to find the amplitude and phase functions:

To get decibels (dB), you compute 20 log (|G(w)|), and f(w) must be converted from radians to degrees.