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Does this solution exhibits resonance

  1. Dec 23, 2005 #1
    In a question, I've been asked to find the general solution of the equation:

    [tex] \ddot{x} + \omega^2{}_{0} = cos( \omega t) [/tex]

    [tex] (\omega , \omega_{0} > 0, \omega \neq \omega_{0})[/tex]

    I've found the solution to this.

    It then asks me if this solution exhibits resonance. What does this mean and how do you determine this?
  2. jcsd
  3. Dec 23, 2005 #2


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    If you found the solution then it should be apparent whether it exhibits resonance. It might be helpful if you displayed your solution here.

    Incidentally, if you have excluded the possibility of [itex]\omega = \omega_0[/itex] then you have excluded the possibility of [exact] resonance! :)
  4. Dec 24, 2005 #3
    Ok, this is my answer:

    [tex] x = A sin( \omega_{0}t) + B cos (\omega_{0}t) + \frac {1} {\omega_0^2 - \omega^2} cos (\omega t) [/tex]
    Last edited: Dec 24, 2005
  5. Dec 24, 2005 #4
    Last edited: Dec 24, 2005
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