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I have a set of displacement-time graphs from an experiment to convert to the frequency domain. Both the Fourier and Laplace transform seem to do this, so what's the difference between them (difference in end result, not the mathematical difference) Also, is there even a way to perform a Laplace transform and output a graph?

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The Fourier transform will better represent your data if there are oscillations in the displacement- time graphs and you want the period of those oscillations. The Laplace transform will better represent your data if it is made up of decaying exponentials and you want to know decay rates and other transient behaviors of your response.

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  • $\begingroup$ Thanks, so if I have a damped sine wave, what should I expect as the output of a Laplace transform? $\endgroup$ Dec 6, 2017 at 7:22
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    $\begingroup$ You would get a Lorentzian shifted by the decay rate. You can just look it up in a table, like the one here: en.m.wikipedia.org/wiki/List_of_Laplace_transforms $\endgroup$
    – KF Gauss
    Dec 6, 2017 at 7:54
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    $\begingroup$ If you do the fourier transform, you will also get a Lorentzian, but it will be shifted by the sine wave frequency instead of the damping. Again, it depends on your goal here. $\endgroup$
    – KF Gauss
    Dec 6, 2017 at 8:16

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