1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?