solve a second order Differential equation with a forcing function containing multiple harmonics

Dear all,

I need to solve a second order ODE shm by numerical integration. It contains a forcing function with multiple harmonics of cosine function.Can anyone suggest an appropriate numerical method and how to implement it in matlab?

Regards.

Answer 1

[Jarrod Rivituso]

I believe you can do this with any of the ode solvers.

http://www.mathworks.com/help/techdoc/ref/ode23s.html

One thing to note is that you need to convert the second order ODE to a system of two first order ODEs and explicitly solve for the derivative terms. For instance, the equation

a*x'' + b*x' + c*x = cos(3*pi*t) + cos(4*pi*t)

would become the two equations

x(2)' = (1/a) - b*x(2) - c*x(1) + cos(3*pi*t) + cos(4*pi*t) x(1)' = x(2)

Then, you can easily write the derivative function that the ODE solvers require:

function dx = derivs(t,x)
a = 1;
b = 1;
c = 1;
dx = zeros(2,1);
dx(1) = x(2);
dx(2) = (1/a) - b*x(2) - c*x(1) + cos(3*pi*t) + cos(4*pi*t)

[Shravan Chandrasekaran]

Hi Jarrod,

I tried the state space form and ode45. but my response turns out to be in single harmonic which is not feasible.am unable to sort where the mistake is!

Regards.

[Jarrod Rivituso]

Good luck. Have you tried varying the intensities of the forcing functions?

[Shravan Chandrasekaran]

Hi Jarrod, It was the forcing function intensity. I have a periodic response which is also multi harmonic but it keeps drifting away from time axis with increase in time. Any suggestions ?

[Jarrod Rivituso]

You'd have to tell me what the equation is. I'd assume it has something to do with the dynamics of the ODEs.

You could try changing the phase of the forcing functions to see if that changes anything. I've seen similar "drifts" before that had to do with that.