## Bode plot for nonlinear equation

Asked by Alberto Manzanero

### Alberto Manzanero (view profile)

on 8 Nov 2017
Latest activity Answered by Aveek Podder

### Aveek Podder (view profile)

on 24 Nov 2017
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

### Aveek Podder (view profile)

Answer by Aveek Podder

### Aveek Podder (view profile)

on 24 Nov 2017

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.