Natural frequency determination

This question does not even make sense, do you know what a natural frequency is? Also, what is a transfer frequency functions? Do you mean you have a transfer function, obtained analytically via frequency sweeps?

Side:
Please capitalize the word "I" in sentences.

 

Capitalize "I" when you use it in sentences. Goodness, gracious .

The word for (b/a) is ratio, not ration. Fourier is named after someone, it is capitalized as well. When you type in a proper English sentence, I will try and help you.

 

Resonance occurs when the bode magnitude plot reaches a peak.

 

Rather than give you the answer, I want you to arrive to it on your own. Reflect on the derivation of terms when we define the natural frequency, damping ratio, etc, for any classic single input, single output (SISO) system. Hint: look at the equations of motion in those cases. What can you say about them? How does that apply to your complex system?

 

When I don't know the values in my system (ie mass compliance, damping), I often modify a known value (ie mass) and observe the effect. For a second order system, it's easy to ascertain the baseline mass based upon the added mass and frequency shift.

Then, knowing the baseline mass and the baseline resonance, you can compute the compliance.

Of course it gets much more tricky if you're coupled into another system....

 

You are getting close to what I'm hinting at.