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Fourier series, is this valid?

  1. Apr 20, 2015 #1
    Hi, I have a Fourier problem that i do not know if it is valid to do the calculations like this.

    The Fourier transform looks like this
    ##
    \hat{v}(x,\omega) = \frac{\hat{F}(\omega)}{4(EI)^{\frac{1}{4}}i \omega^{\frac{3}{2}}(\rho A)^{\frac{3}{4}}}\left[ e^{-i\left[\omega^2 \frac{\rho A}{EI} \right]^{\frac{1}{4}}x} -ie^{-\left[\omega^2 \frac{\rho A}{EI} \right]^{\frac{1}{4}}x} \right]##

    and is the Fourier transform of a displacement for a wave in a beam.
    The inverse Fourier transform of this equation is the displacement and is displayed below

    ##v(x,t)= \sum_n\hat{v} \cdot e^{i\omega t}##

    What I want to calculate is the x derivative of ##v(x,t)##. Is it valid to calculate ##\frac{\partial \hat{v}}{\partial x}## and do a inverse Fourier transform to get ##v^\prime(x,t)##

    In other words, is this valid
    ## v^\prime(x,t) = \sum_n \hat{v}^\prime \cdot e^{i \omega t}##
     
  2. jcsd
  3. Apr 21, 2015 #2

    DrClaude

    User Avatar

    Staff: Mentor

    I don't see any problem with what you wrote.
     
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