3. What is the partial fraction decomposition of the Laplace transform F(s) = A) B) B C A + + s+1 (s + 1)² s-1 B A A) B) + S+1 (s + 1)² A Bs + C C) s+1 s² - 1 D) A and B only 1 4. What is the inverse Laplace transform of the function given in number 3? 1 1 e- - xe + ex 4 III 1 1 1 e-x +zxe C) D) + 1 e-xxe* + 0 1 4 ex 1 (s + 1)(s² - 1) ?
3. What is the partial fraction decomposition of the Laplace transform F(s) = A) B) B C A + + s+1 (s + 1)² s-1 B A A) B) + S+1 (s + 1)² A Bs + C C) s+1 s² - 1 D) A and B only 1 4. What is the inverse Laplace transform of the function given in number 3? 1 1 e- - xe + ex 4 III 1 1 1 e-x +zxe C) D) + 1 e-xxe* + 0 1 4 ex 1 (s + 1)(s² - 1) ?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
PLEASE ANSWER #4,5&6
Transcribed Image Text:1. Which of the following statements is/are true?
I. The Laplace transform of f(t) is given by the proper integral L{f(t)}
Inverse Laplace Transform also exhibits linearity.
II.
A)
B)
2. Find the inverse Laplace transform of F(s)
Statement 1 only
Statement 2 only
A) 3 sin t
B)
A)
B)
3et sin t
A)
B)
A
s+1
A
+
+
s+1 (s + 1)²
4
1
4
B
C
+
(s + 1)² S-1
B
e
3. What is the partial fraction decomposition of the Laplace transform F(s) =
-x
-* +
xe
-x
4
=
A) 2 cos 3x - 6 sin 3x
B)
2 cos 3x - 2 sin 3x
A) Always true
B) Always false
D)
ex
s² -
4. What is the inverse Laplace transform of the function given in number 3?
1
1
1
1
2
+=ex
4
2
1
1
2xe
C)
D)
C)
D)
Both statements
None of the choices
3
2s + 2
C)
D)
3sin (t + 1)
None of the choices
C)
D)
?
A
s+1
A and B only
C)
D) 0
1
+
Bs + C
s² - 1
2s6
5. What is the inverse Laplace transform of the given function F(s) =
s² +9
1
xex + ·ex
4
=
2
2
cos 3x - sin 3x
3
3
cos 3x2 sin 3x
Sometimes true
None of the choices
+∞
fe-stj
e-st f(t) dt.
1
(s + 1)(s² - 1)
?
6. The properties of Laplace transform (discussed in class) are all applicable for inverse Laplace
transforms.
?
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