solve a second order Differential equation with a forcing function containing multiple harmonics
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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.
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Jarrod Rivituso
2011-4-18
I believe you can do this with any of the ode solvers.
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)
4 个评论
Shravan Chandrasekaran
2011-4-18
Jarrod Rivituso
2011-4-18
Good luck. Have you tried varying the intensities of the forcing functions?
Shravan Chandrasekaran
2011-4-20
Jarrod Rivituso
2011-4-20
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.
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2011-4-18
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