Assume the function f(t) has a Fourier transform given by F[f](w) = ²1 HINT: Use Euler's identities. What is the value of the integral Sdte ut f(t) O Cannot be computed with the given information O 0.5 3.5 +1 5) What is the value of the integral Sdte 13.5t f(t) O Cannot be computed with the given information O 0.5 What is the value of the integral Sdte 13.5t f(2) O Cannot be computed with the given information O 0.5 3.5²+1 2.2 7.7²+1 O ∞ 0 0 0 0 2.2 3.5 +1 O 1+w² 7.7² +1
Assume the function f(t) has a Fourier transform given by F[f](w) = ²1 HINT: Use Euler's identities. What is the value of the integral Sdte ut f(t) O Cannot be computed with the given information O 0.5 3.5 +1 5) What is the value of the integral Sdte 13.5t f(t) O Cannot be computed with the given information O 0.5 What is the value of the integral Sdte 13.5t f(2) O Cannot be computed with the given information O 0.5 3.5²+1 2.2 7.7²+1 O ∞ 0 0 0 0 2.2 3.5 +1 O 1+w² 7.7² +1
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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Transcribed Image Text:Assume the function f(t) has a Fourier transform given by Ff(w) = ²1
HINT: Use Euler's identities.
a)
What is the value of the integral
Sdte iwt f(t)
O Cannot be computed with the given information
3.5 +1
b)
What is the value of the integral
Sdte 13.5t f(t)
O Cannot be computed with the given information
c)
What is the value of the integral
fdte 13.5t f(2)
O Cannot be computed with the given information
O
3.5 +1
2.2
7.741
O 0.5 O ∞
O 0.5 O ∞
O 0.5
2.2
3.5 +1
O
O
-
1+w²
7.72 +1
![d)
What is the value of the integral
f dt cos (3.5t)f()
O Cannot be computed with the given information
e)
[D/HD] Imagine now that
Calculate the integral
Sdt (3 cos (3.5mt) + 1 sin (3.5t)) f(t+6)
3 cos (21)+1 sin (21)
3+1
3.5²41
3.5 +1
3.5 +1
2.2
7.7² +1
O Cannot be computed with the given information
2.2
7.7 +1
=
3 cos (3.5 t) + 1 sin (3.5t)
○ cos (7.7) 35²41
y(t)
3e¹21+le 121
3.5²+1
00
O cos (7.7) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53ce1657-b18a-4e5a-99aa-3e87bdade9e3%2Fba007248-fdd7-41bf-9afc-081fff7447be%2Frwk5ino_processed.png&w=3840&q=75)
Transcribed Image Text:d)
What is the value of the integral
f dt cos (3.5t)f()
O Cannot be computed with the given information
e)
[D/HD] Imagine now that
Calculate the integral
Sdt (3 cos (3.5mt) + 1 sin (3.5t)) f(t+6)
3 cos (21)+1 sin (21)
3+1
3.5²41
3.5 +1
3.5 +1
2.2
7.7² +1
O Cannot be computed with the given information
2.2
7.7 +1
=
3 cos (3.5 t) + 1 sin (3.5t)
○ cos (7.7) 35²41
y(t)
3e¹21+le 121
3.5²+1
00
O cos (7.7) =
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