I have two root locus plots (x-real, y-imaginary) of the same oscillating mode: (1) for a base case system and (2) a system with added feedback. They are so similar, almost identical that I am having a hard time interpreting it but the author comments that "the frequency of the mode has been hardly changed". So he concludes it has not been changed significantly but how can he tell? Is it because the root locus has not moved along the imaginary axis?
On a root locus, zeroes and poles are plotted. What could be changed about these zeroes and poles without changing the frequency of the mode?