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What Magnitude(db) and Phase(deg) represent on Bode Diagram?

I am working on 2 DOF System and I want to understand some basic things.

Below (on the picture) you can see the system, the transfer function and the bode plot.

I can't understand what exactly these values mean.

Magnitude 26.4269 (dB) - Resonant Frequency 5.2493 (rad/s) % Results of the First Peak
Magnitude 2.2837 (dB) - Resonant Frequency 37.8886 (rad/s) % Results of the Second Peak

The First Pick represent the highest vibration of Numerator = X1(s)-X2(s)?

The Second Pick represent the highest vibration of Denominator = W(s)?

Magnitude(db) is the "volume" of my system?

Aim is possitive or negative Magnitude(db) for my system?

and what about Phase (deg)?

2 DOF - Transfer Function - Bode Plot - Equations

[NEW]

Magnitude (abs) vs Frequency (rad/s)

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Your transfer function appears to be representing the relative displacement between $M_1$ and $M_2$ as a result of an input excitation, $W$, presumably a force. This simplified linear model is often used to express the dynamics of an automotive suspension system where $M_1$ is the mass of the vehicle and $M_2$ is the mass of the suspension mechanism and vehicle tire.

The lowest frequency , under-damped peak is presumably dominated by the suspension dynamics relative to the vehicle, and the higher frequency, underdamped peak (actually just a cutoff frequency & very little peaking) is dominayed by the dynamics relative to the contact with the road.

A transfer function in the LaPlace variable, $s$ , or complex frequency provides a measure of response, and that can be graphically shown by taking the magnitude and phase of the transfer function evaluated over a range of real frequency.

That's what it all means in terms of a physical explanation, but I suspect you are trying to ask a different question, and its just not clear to me what that might be.

Is this a homework problem?

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  • $\begingroup$ Comment (1/2): Thanks for your answer. Yes this is a homework exercise. To be honest I don't know what to ask. They have just given us the 2 DOF System and told us to find the Amplitude(m) - Frequency(Hz) Diagram. This Diagram shows the Resonant Frequency of Body Mass and the Resonant Frequency of Suspension Mass. For example, at 1 Hz the Body Mass vibrating very much and the Suspension Mass very little but at 10 Hz the Body Mass vibrating very little and the Suspension Mass very much. $\endgroup$ – Bob Apr 4 '16 at 7:14
  • $\begingroup$ Comment (2/2): Anyway, I have used matlab to solve my problem and I found this Bode Plot which seems similar to the Diagram that I need and I thought that may be what I am looking for in different units (dB instead of m). $\endgroup$ – Bob Apr 4 '16 at 7:15
  • $\begingroup$ I have some equations from my notes (which I have attached them above) but I am not sure if it is correct. I tried to solve them with my hand but I got lost. $\endgroup$ – Bob Apr 4 '16 at 7:23
  • $\begingroup$ @Bob Matlab plots can be expressed in either linear, log or dB - so that shouldn't be a problem. You should be able to express in m if you like, its just that log units or decibels are more often convenient since they compress an otherwise wide dynamic range on a linear scale. What was particularly confusing to me is what you said: "Magnitude(db) is the "volume" of my system?" $\endgroup$ – docscience Apr 4 '16 at 20:33
  • $\begingroup$ @Bob yes - when you have multiple degrees of freedom and/or the order of the system becomes much larger than two its very easy to make mistakes in the algebra. I find it better to just use a symbolic solver like Macsyma (or the freeware version Maxima) or MathCAD from PTC. $\endgroup$ – docscience Apr 4 '16 at 20:36

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