Bode plot for nonlinear equation

Hello,

I want to plot the bode diagram for nonlinear equation. The equation is:

 dxdt_2 = -c*x(2)-k*x(1)-b*(x(1)^3)+ F*sin(w*t+phi)

I have used this code:

 t  = 0:0.001:250;   % time scale
c  = 0.1;
k  = 1;
b =0.5;
x0 = 0.1;
v0 = 0.1;
F=0.2;
phi=0;
w=10;  
i= 0;

    [t,x] = ode45( @rhs, t, [x0,v0]);

function dxdt=rhs(t,x)

        dxdt_1 = x(2);
        dxdt_2 = -c*x(2)-k*x(1)-b*(x(1)^3)+ F*sin(w*t+phi) ;

        dxdt = [dxdt_1 ; dxdt_2];  
  end

How can I plot the Bode Diagram for this function?

Thank you

Answer 1

[Aveek Podder]

Hi,

You can use the 'fft' command of MATLAB to find the frequency analysis of the impulse response for the function and plot Magnitude and phase in 'semilogx' plot. But the response will be dependent on the initial conditions.