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Second order ODE solution for this system?

  1. Feb 28, 2009 #1
    second order ODE solution for this system??

    hello guys,
    I am wondering if what is the analytical solution for this system?
    can we solve it as a mass-spring-damper system?
    thanks for your helps.
    the rectangular part is removed from the disk.

    [URL=http://img3.imageshack.us/my.php?image=odev.jpg][PLAIN]http://img3.imageshack.us/img3/3610/odev.th.jpg[/URL][/PLAIN]
     

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  3. Feb 28, 2009 #2
    Re: second order ODE solution for this system??

    So the DE is

    ax'' + bx' + cx = 0

    Write the characteristic equation...

    an^2 + bn + c = 0

    Solve for n using the quadratic formula...

    n = [-b +- sqrt(b^2 - 4ac)] / 2a

    This will give you two (possibly non-unique) exponents. if the exponents are different, say n1 and n2, then the solution is

    x(t) = Aexp(n1 t) + Bexp(n2 t)

    If the exponents are the same, then

    x(t) = Aexp(n t) + B t exp(n t)

    Am I missing something, or does this answer your question?
     
  4. Mar 1, 2009 #3
    Re: second order ODE solution for this system??

    thanks a lot, that is the answer if the motion is linear, how about the angular motion?
    how can i modify this equation.??
     
  5. Mar 1, 2009 #4
    Re: second order ODE solution for this system??

    To make it angular, rewrite it using "theta" instead of "x".
     
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