That was a horrible mistake. I had something like this:
allroots: expected a polynomial; found [abs(ws)=(10479*abs(ws))/(10985*sqrt(ws^2-1))]
Simplifying |ws| resulted in:
float(solve(1=k/sqrt(ws^2-1)));
[ws=-1.44876,ws=1.44876]
Indeed, the quick scribbling (not an excuse) made me read "1/k" instead of "k". Mea culpa. However, this still isn't an answer to the problem so the question remains.
Regards,
Vlad.