(a) Calculate the inverse Fourier transform h(x) of h(k), where h(k)= 0 for b for -b for 0 for k<-a, a a, and a, b are some real positive constants. Express your final answer in terms of sines and/or cosines (as opposed to exponentials).
(a) Calculate the inverse Fourier transform h(x) of h(k), where h(k)= 0 for b for -b for 0 for k<-a, a a, and a, b are some real positive constants. Express your final answer in terms of sines and/or cosines (as opposed to exponentials).
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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please help me out. details and explanations are very much appreciated
![3.
(a) Calculate the inverse Fourier transform h(x) of h(k), where
(b)
(c)
h(k)=
0
for
b for
-b for
0 for
and a, b are some real positive constants. Express your final answer in
terms of sines and/or cosines (as opposed to exponentials).
where
With the help of Table 1, determine the inverse Laplace transform f(t)
of
is a Heaviside function.
k<-a,
a <k<0,
0<k<a,
k > a,
F(s) =
Using the method of Laplace transform, solve the following initial value
problem:
e-7(+2)
(s+ 2)² - 25
ÿ + 5y + 6y = (sin t)[H(t) - H(t-2n)],
y(0) = 0,
y (0) = 0,
H(t-a)=
for t > a,
10 fort <a,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae7db2c1-de5d-4f19-9087-8da1bfe4b1c5%2Fcaed92cc-f5b9-4722-8bf8-f42512686271%2Fsl9kvxxl_processed.png&w=3840&q=75)
Transcribed Image Text:3.
(a) Calculate the inverse Fourier transform h(x) of h(k), where
(b)
(c)
h(k)=
0
for
b for
-b for
0 for
and a, b are some real positive constants. Express your final answer in
terms of sines and/or cosines (as opposed to exponentials).
where
With the help of Table 1, determine the inverse Laplace transform f(t)
of
is a Heaviside function.
k<-a,
a <k<0,
0<k<a,
k > a,
F(s) =
Using the method of Laplace transform, solve the following initial value
problem:
e-7(+2)
(s+ 2)² - 25
ÿ + 5y + 6y = (sin t)[H(t) - H(t-2n)],
y(0) = 0,
y (0) = 0,
H(t-a)=
for t > a,
10 fort <a,
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