Solving a second order differential equation with matlab.

Hey,

I wanted to plot a second order differential equation in Matlab to see how it would look. The equation is the following:

y = x + 2*cos(omega)*y'-y''

This equation corresponds to an IIR filter with the poles on the unit circle. I will be using it to generate harmonic oscillations.

"x" only gives a unit impulse, and omega = 2*pi*(f0/fs), and is used to control the oscillations.

Please show me what I should write to be able to see these oscillations in Matlab.

Thanks in advance.

Answer 1

[madhan ravi]

syms y(x)
dy=diff(y);
dy2=diff(y,2);
omega=5; %your value acheived by 2*pi*(f0/fs) formula
ode=y == x + 2*cos(omega)*dy-dy2 ;
vars = y(x);
V = odeToVectorField(ode)
M = matlabFunction(V,'vars', {'x','Y'})
interval = [0 10];  %time interval
y0 = [0 0];      %initial conditions
ySol = ode45(M,interval,y0);
tValues = linspace(interval(1),interval(2),1000);
yValues = deval(ySol,tValues,1); %number 1 denotes first solution likewise you can mention 2 for the next solution
plot(tValues,yValues)
hold on
yValues = deval(ySol,tValues,2); 
plot(tValues,yValues,'r')

[Marius Turcan]

Thank you for your answer.

It is working, and producing the same plot you've provided.

I have a follow-up question, which is how would I go from here if I want to see a continuous evaluation of the oscillations produced, the same way you would see on an oscilloscope?

Would I be better off implementing the corresponding filter in Simulink and viewing that way?

[madhan ravi]

Would I be better off implementing the corresponding filter in Simulink and viewing that way?

I have no experience with simulink.. but I am pretty sure it's more handy to simulate