# Homework Help: Fourier series, is this valid?

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1. Apr 20, 2015

### Trevorman

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. Apr 21, 2015

### Staff: Mentor

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