Symbolic solution to filter magnitude frequency response

Hi all,

please see attached.

I am attempting to derive what I thought would be a simple enough equation to describe the maxima and/or minima of a "filter" function magnitude response.  The example is a simplified version of my original problem and although in this case the answer is very obvious (w = 1), my original problem did not have so obvious an answer,  And also, although I can easily plot the response, I would like to establish the design equations to allow me to work backwards from a requirement to a solution in equation form.

In the worksheet, the symbolic solution seems to fail.  I specify the function H(s) and then substitute s = 1i.w to obtain continuous frequency response.  I suspect the problem is complicated by the use of the |magnitude| function which might make symbolic solution difficult - that's my guess at why this doesn't seem to work.  If there is a better way then please let me know!  I have been staring at this on and off for a few days so might be missing the obvious.

Thanks in advance,

D