# Mathieu oscillator: parametric resonance

1. Feb 20, 2010

### samreen

hey, i need help in solving the equation of a mathieu oscillator (ignoring damping) and showing how the condition for max parametric resonance is doubling of the natural frequency . ( got viva 2morro. im so going to suck)

D^2x + K(t)x =0
(Ko is the constant natural frequency when no perturbation present. D^2 is the second order time derivative of displacement x) . and, um, i kno precious little maths. for differential equations with variable coeffs, jst Frobenius method to seek series solns.

2. Feb 20, 2010

### masqau

if ur
K(t)=a-2q cos(2t)
than ur differential equation is Matthieu differential equation.

3. Feb 20, 2010

### samreen

yes it is. but i need to develop that solution for the viva

4. Feb 21, 2010

### masqau

5. Feb 21, 2010

### samreen

hey, brilliant! thanx

6. Feb 21, 2010

### masqau

U welcome

7. May 10, 2011

### babamarysol

Hi masqau,
can you explain me the procedure that i found in your first link

http://eqworld.ipmnet.ru/en/solutions/ode/ode0234.pdf

"Selecting a sufficiently large m and omitting the term with the maximum number in the recurrence relations we can obtain approximate relations for the eigenvalues a (b) with respect to parameter q. Then, equating the determinant of the corresponding homogeneous linear system of equations for coefficients A (B) to zero, we obtain an algebraic equation for finding a(q) (or b(q))"

I try to put into practice but without success :-(

8. May 10, 2011

### masqau

Last edited by a moderator: Apr 25, 2017
9. May 11, 2011

Thanks