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Mathieu oscillator: parametric resonance

  1. Feb 20, 2010 #1
    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. jcsd
  3. Feb 20, 2010 #2
    if ur
    K(t)=a-2q cos(2t)
    than ur differential equation is Matthieu differential equation.
  4. Feb 20, 2010 #3
    yes it is. but i need to develop that solution for the viva
  5. Feb 21, 2010 #4
  6. Feb 21, 2010 #5
    hey, brilliant! thanx
  7. Feb 21, 2010 #6
    U welcome
  8. May 10, 2011 #7
    Hi masqau,
    can you explain me the procedure that i found in your first link


    "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 :-(
  9. May 10, 2011 #8
    Last edited by a moderator: Apr 25, 2017
  10. May 11, 2011 #9
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