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Homework Help: Forier transform

  1. Jul 5, 2007 #1


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    1. The problem statement, all variables and given/known data
    it's related with SHM.its a trivial question.and it's definitely got an ans.i need to do fourier transformation for
    e(iwt) e-(q**2/bk(2sin**2(wt)/2))dt.
    btw the limits -inf to +inf.whereb=kt,k=boltzmannconst.w=(k/m)**.5(k here is spring const.)do fourier transform and get it in terms of frequency

    2. Relevant equations
    that"s the only eqnbut can be modified to e-x*e-(x*coswt) where x=const.
    ("though some friends say it'll result in error function")
    3. The attempt at a solution

    =e-(q**2/bk(1-coswt)) (taking q**2/bk=const.say x)
  2. jcsd
  3. Jul 5, 2007 #2


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    It's really hard to read the function you're trying to calculate the FT for. Are you saying that the function is

    [tex] f(t) = \exp{\left(-\frac{q^2}{bk} \frac{2\sin^2(wt)}{2}\right)} [/tex]

    and you want to calculate the Fourier transform?

    [tex] \hat{F}(\omega) = \int_{-\infty}^{\infty} \exp{\left(-\frac{q^2}{bk} \frac{2\sin^2(wt)}{2}\right)} \exp{(-i \omega t)} dt [/tex]
    Last edited: Jul 5, 2007
  4. Jul 5, 2007 #3


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    the given eqn is

    where b=kT,T=absolute temp,k=bolzmann const. and w=(k/m)^(1/2) t=time period.

    the above fn. depends on time.i have to apply fourier transform to convert it into "w" frequency.

    the alternate method i came up with is by treating "q,b,w" as const. say"x"
    and converting sin^2(wt/2) as "1-coswt"

    so the final eqn became e-(x(1-coswt))
    other wise have to fourier transform for this eqn.
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