title: How can I get the Resonant Frequencies (Bode plot)? (Response of 2-DOF System)
body: <p>I want to study the response of the system.</p>
  
  <p>I want to find the resonant frequency of the sprung mass (m1) and the resonant frequency of the unsprung mass (m2).</p>
  
  <p>Because I am not sure if I have understood the meaning of resonant. Let's say that we have a suspension system and we stimulated with a step response 0.1(m).</p>
  
  <p>That means, for example at 1(Hz) the sprung mass (m1) vibrating at the high level? and at 10(Hz) the unsprung mass (m2) vibrating at the high level?</p>
  
  <p>I've read about bode plot and I did some things as you can see below but I don't know if this is the way to find the Resonant Frequencies. Maybe FFT is what I'm looking for?</p>
  
  <p>In my bode plot (Picture below):</p>
  
  <p>Blue Line: The first peak corresponds to the resonant frequency of the sprung mass (m1)? and Orange Line: Τhe second peak (which is higher than the first peak of orange line) corresponds to the resonant frequency of the unsprung mass (m2)?</p>
  
  <p>If yes how can I get these values? What I need to add to my code?</p>
  
  <p>Can I change the units from decibel to m?</p>
  
  <pre><code>clc;
  clear all;
  close all;
  
  %% Parameters
  m1 = 400;    % Sprung Mass (kg)
  m2 = 40;     % Unsprung Mass (kg)
  k1 = 21000;  % Suspension Stiffness (N/m)
  k2 = 150000; % Tire Stiffness (N/m)
  b1 = 1500;   % Suspension Damping (N*s/m)
  b2 = 0;      % Tire Damping Coefficient (N*s/m)
  
  %% Transfer Function
  num1 = [(0) (0) (b1*b2) (b1*k2+b2*k1) (k1*k2)];
  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)/Xr(s)
  num2 = [(0) (m1*b2) (m1*k2+b1*b2) (b1*k2+b2*k1) (k1*k2)];
  den2 = [(m1*m2) (m1*b1+m1*b2+m2*b1) (m1*k1+m1*k2+m2*k1+b1*b2) (b1*k2+k1*b2) (k1*k2)];
  G2 = tf(num2,den2); % G2(s) = X2(s)/Xr(s)
  
  %% Results
  figure;
  step(0.1*G1,0:0.01:5);
  hold on;
  step(0.1*G2,0:0.01:5);
  title('');
  legend('m1','m2');
  xlabel('Time (s)');
  ylabel('Amplitude (m)');
  axis([]);
  grid on;
  
  figure;
  bode(G1);
  hold on;
  bode(G2);
  title('');
  legend('m1','m2');
  axis([]);
  grid on;
  </code></pre>
  
  <p><a href="http://i.stack.imgur.com/l4eKm.png" rel="nofollow">Reaponse, Bode Plot and 2 DOF System</a></p>