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

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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.

%%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;

##### 0 Comments

### Accepted Answer

Star Strider
on 31 Mar 2016

##### 16 Comments

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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