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Soln to 2nd ODE nonhomgeneous

  1. Mar 8, 2005 #1
    Can anyone give me a hand with this, cause I'm stumped and can't remember exactly how to go about solving this.

    here's the eqn

    m[d^2x/dt^2 + wsubo^2 x] = F cos wt

    I'm supposed to show that x(t) = xsubo cos wt

    w is the incident freq
    wsubo is the resonant freq
    m is mass

    it's from physics but the principles are just maths.
  2. jcsd
  3. Mar 8, 2005 #2
    Since you are given the solution, just plug it in to the eqn. I get a solution only when [tex]x_0=\frac{w^2-F}{w^2}[/tex].
    Last edited: Mar 8, 2005
  4. Mar 8, 2005 #3
    I would have thought you would have to work with undetermined coefficients or something
  5. Mar 8, 2005 #4


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  6. Mar 8, 2005 #5


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    No, you were not asked to SOLVE the equation, only to show that
    x(t) = x0 cos wt IS a solution.
  7. Mar 8, 2005 #6
    I just found this out, by plugging in xsubocoswt, I got F = m (wsub0^2 - w^2) x

    by then using undetermined coefficients I get a value of

    y(t) = F / m (wsub0^2 - w^2) coswt

    by substituting F in I get the xcos wt
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