Answered: a) Find the Fourier transform of f(t) =… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

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Question

Solve (a) ,(b)

a) Find the Fourier transform of
4
f(t) = e-tu(t) + t² +9°
b) Solve the following differential equation using Fourier Transform methods:
dy
+ 5y = 38(t).
dt
c) Let f(t) = u(t)e¯4t and g(t) = √(t — 2).
i) Write out the expression for the convolution of these two functions, i.e., y(t) = f * g(t), as an integral.
-2jw
e
ii) Show the Fourier transform of y(t) is given by Y (w) =
= 4+jwⓇ
iii) Invert this last expression to solve your integral and find y(t). Explain your methodology.

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