1. Limited time only! Sign up for a free 30min personal 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!

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


    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

    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:

    Last edited: Mar 15, 2007
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook