I have the following situation and would like some feedback on my approach to solving the problem, since I am not sure if it's "mathematically legit":
I have two transfer functions: function A is the transfer function of a system, function B is the transfer function of a reduced version of the same system. The transfer functions show the frequency response of the system, the input being a force and output being a displacement. I want to compare both functions and see what the deviation of the reduced order system is from the original system.
Now, however, for the overall goal of the project, I am not so interested in the displacement, but rather the velocity. So it would be great if I could compare the velocities I am getting from both functions. This should just be the derivative of the transfer functions since the transfer functions are giving me the displacement? The transfer functions are complex and in the frequency domain (Ha(jw) and Hb(jw)), so the derivative of these should just be a multiplication with jw (since s=jw for steady state)? Is this correct?
Thank you in advance!