# Determining damping ratio empirically?

I'm an engineering coop at a vibrations consultant. I was given a graph plotting a series of applied frequencies against a floor's acceleration response to them. I was asked to find the natural frequency and damping ratio, but I haven't been able to find the damping ratio. I've taken a course in vibrations, but we were always given more about the scenario (mass of the object, spring constant, etc.). I've asked him to at least give me a starting point, but he's refused.

My boss also asked me to find the theory behind how the damping ratio is determined empirically. All the resources I've found online either reiterate what I already learned in my courses, or are so advanced that I can't even begin to understand them.

My questions are: how is the damping ratio determined empirically, and what is the general way to solve this problem?

For context, my vibrations course focused on 1 DOF systems, teaching the basics behind damping ratio, natural frequency, and general vibrations. We did questions about base excitation and rotating imbalances in machinery.

• What does: "I was given a graph plotting a series of applied frequencies against a floor's acceleration response to them" mean exactly? Do you have a frequency response function (both amplitude and phase or amplitude only) describing the systems response? Do you have the raw data behind the graph? Anyway, for a quick estimate (I can write an answer later) google: Q-factor and/or 3dB bandwidth. Jul 5 '17 at 5:26