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Homework Help: Need the correct time dependent function

  1. Mar 15, 2007 #1
    1. The problem statement, all variables and given/known data

    The equation of motion of a free electron in an electric field is

    m((d^2)x)/(dt^2) = -eE (Eq. 1)

    If x and E have the time dependence exp(iwt), where w=angular frequency, then

    -(w^2)mx = -eE (Eq. 2)

    What does the time dependent function whose second derivative equals -(w^2)x look like?

    3. The attempt at a solution

    I know from my papers that the electromagnetic wave is given by

    E=E0exp(iwt),

    and I guess the equation I'm after looks similar. The second derivative of x*exp(iwt) would give me the correct answer, but x=x0*exp(iwt) doesn't seem to do, because equation 2 says x and not x0.
     
  2. jcsd
  3. Mar 15, 2007 #2
    x=x0exp(iwt)

    d2x/dt2=-w^2 x0 exp(iwt) = -w^2 x
     
  4. Mar 15, 2007 #3
    Ah, I forgot that the factor exp(iwt) will still be there after the derivation :rolleyes:

    Thanks!
     
    Last edited: Mar 15, 2007
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