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

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Bob
Bob on 31 Mar 2016
Commented: Star Strider on 4 Apr 2016
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.
%%Parameters
m1 = 2500; % (kg)
m2 = 320; % (kg)
k1 = 80000; % (N/m)
k2 = 500000; % (N/m)
b1 = 350; % (N*s/m)
b2 = 15020; % (N*s/m)
%%Transfer Function
num1 = [(0) (-m1*b2) (-m1*k2) (0) (0)];
den1 = [(m1*m2) (m1*b1+m1*b2+m2*b1) (m1*k1+m1*k2+m2*k1+b1*b2) (b1*k2+k1*b2) (k1*k2)];
G1 = tf(num1,den1); % G1(s) = (x1(s)-x2(s))/w(s)
Below you can see the Transfer Function and Bode Diagram results.
G1(s) = (x1(s)-x2(s))/w(s)
Magnitude 26.4269 (dB) - Resonant Frequency 5.2493 (rad/s)
Magnitude 2.2837 (dB) - Resonant Frequency 37.8886 (rad/s)
I can't understand what exactly these values mean.
For instance the first peak represent the vibration of the numerator x1(s)-x2(s) and the second peak the vibration of the denominator w(s)?
Magnitude(db) is the volume? the high level of vibration of my system?
Aim is possitive or negative Magnitude(db) for my system?
and what about Phase (deg)?
%%Parameters
m1 = 2500; % (kg)
m2 = 320; % (kg)
k1 = 80000; % (N/m)
k2 = 500000; % (N/m)
b1 = 350; % (N*s/m)
b2 = 15020; % (N*s/m)
%%Transfer Function
num1 = [(0) (-m1*b2) (-m1*k2) (0) (0)];
den1 = [(m1*m2) (m1*b1+m1*b2+m2*b1) (m1*k1+m1*k2+m2*k1+b1*b2) (b1*k2+k1*b2) (k1*k2)];
G1 = tf(num1,den1); % G1(s) = (x1(s)-x2(s))/w(s)
%%Bode Plot (Magnitude dB - Frequency rad/s)
bode(G1)
grid on;

Accepted Answer

Star Strider
Star Strider on 31 Mar 2016
Both peaks represent complex zeros (roots) of the denominator polynomial (in a transfer function), called poles. (The amplitude will go toward zero in the region of the complex roots of the numerator polynomial, called zeros.) Those roots occur at a particular complex resonant frequency, so looking at them projected on the complex frequency axis (and not the rest of the complex plane), they will have particular magnitudes (here, amplitudes of oscillation of the two masses) at the associated frequencies (frequencies of oscillation of the two masses).
  16 Comments
Star Strider
Star Strider on 4 Apr 2016
My pleasure.
No worries — I needed to review some of these functions, and you gave me the opportunity. This is obviously a homework assignment, so I was reluctant to offer too much help. That would give you an unfair advantage.
The bodeplot function lets you change some of the parameters of the plot that the bode function does not.

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