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a) Find the Fourier transform of f(t) = e-tu(t) + 4 t² +9.

a) Find the Fourier transform of f(t) = e-tu(t) + 4 t² +9.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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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