The Fourier transform of a function f (x) is defined as:f (w) = , f(x)e-iax dx-iwx dxSimilarly, the inverse Fourier transform of a function f (x)whose Fourier transform is known is found as:1f(x) = L f (@) e-iwx dwSo, find the Fourier transform f (w) for a> 0 of thefunction given below, and using this result, calculate theinverse Fourier transform to verify the form f (x) given toyou:for x > 0for x < 0-ахf (x) = }

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The Fourier transform of a function f (x) is defined as: f (w) = Lf(x)e¬iwx dx Similarly, the inverse Fourier transform of a function f (x) whose Fourier transform is known is found as: f (x) Lo f (w) e-iwx dw So, find the Fourier transform f (w) for a> 0 of the function given below, and using this result, calculate the inverse Fourier transform to verify the form f (x) given to you: for x > 0 for x < 0 -ax e f(x) = {

The Fourier transform of a function f (x) is defined as: f (w) = Lf(x)e¬iwx dx Similarly, the inverse Fourier transform of a function f (x) whose Fourier transform is known is found as: f (x) Lo f (w) e-iwx dw So, find the Fourier transform f (w) for a> 0 of the function given below, and using this result, calculate the inverse Fourier transform to verify the form f (x) given to you: for x > 0 for x < 0 -ax e f(x) = {

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter3: Oscillations

Section: Chapter Questions

Problem 3.28P

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