4. What is the Laplace transform of the given function f(t) = 2t² cos² (2t)? 2 F(S) =3 2 S3 A) F(S) =3 s² + 16 2 s + 16 + B) F(s) = A) B) F(s) = F(s) =- 2 53 =II 4 A) F(s) = B) F(s) = 5. What is the Laplace transform of the given function f(t) = cos³ (t)? 3 S 3s s² + 1 3 S 2s(s - 16) s² + 16 1 S A) F(s) = B) F(s) = s² + 1 3s +1 4(s² +9) + 6. If the Laplace transform of x³/2 is 3√√π 4 42 (s + 1) √π 4(s + 1)5/2 . s² +9 s(s² + 16) s² + 2s + 16 (s² + 16) 3√π 4s5/2 C) C) D) D) F(s) = F(s) = F(s) = =I 7. Find the Laplace transform of f(t) = (1 + sin 2t cos 2t). s² + 2s + 16 D) F(s) = + C) F(s) = 2s³ - 96 (s² + 16)³ 2s³ - 96 (s² + 16)³ + 4 s² + 1 D) F(s) = 4s s² +9 1 ,then the Laplace transform of t³/²e-t is: 3√√π C) F(S)=5 (s + 1) 4s2 + S - 4 s² +9 3√√π 4(s + 1)5/2 s² + 2s +4 s(s² + 16) s² + 2s + 16 s(s² + 4)
4. What is the Laplace transform of the given function f(t) = 2t² cos² (2t)? 2 F(S) =3 2 S3 A) F(S) =3 s² + 16 2 s + 16 + B) F(s) = A) B) F(s) = F(s) =- 2 53 =II 4 A) F(s) = B) F(s) = 5. What is the Laplace transform of the given function f(t) = cos³ (t)? 3 S 3s s² + 1 3 S 2s(s - 16) s² + 16 1 S A) F(s) = B) F(s) = s² + 1 3s +1 4(s² +9) + 6. If the Laplace transform of x³/2 is 3√√π 4 42 (s + 1) √π 4(s + 1)5/2 . s² +9 s(s² + 16) s² + 2s + 16 (s² + 16) 3√π 4s5/2 C) C) D) D) F(s) = F(s) = F(s) = =I 7. Find the Laplace transform of f(t) = (1 + sin 2t cos 2t). s² + 2s + 16 D) F(s) = + C) F(s) = 2s³ - 96 (s² + 16)³ 2s³ - 96 (s² + 16)³ + 4 s² + 1 D) F(s) = 4s s² +9 1 ,then the Laplace transform of t³/²e-t is: 3√√π C) F(S)=5 (s + 1) 4s2 + S - 4 s² +9 3√√π 4(s + 1)5/2 s² + 2s +4 s(s² + 16) s² + 2s + 16 s(s² + 4)
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&7
![1. If L{f(t)} = F(s), then
A)
L{eat f(t)} = F(s + a)
B) L{eat f(t)} = F(sa)
2. What is the Laplace transform of the given function
1/1
A) F(s) == +
S
2 s s² + 16A
1/1 S
B) F(S) = (²+4)
3. Given f(t) = e4t, what is L{t²f(t)}?
1
(s - 4)²
1
A)
B)
A) F(s) =
S3
2
B) F(S)=3
A)
B) F(s) =
F(s) =
(s - 4)²
(s-4)³
4. What is the Laplace transform of the given function f(t) = 2t² cos² (2t)?
2 2s³ - 96
2
1
A) F(S) = -5
A) F(S)
+
B) F(s) =-
=
B) F(s) =
s + 16
S² + 16
2s(s - 16)
s² + 16
S
4 s² +1
3s +1
4(s² +9)
6. If the Laplace transform of x³/² is
3√√π
+
4 s² +9
C)
D)
5. What is the Laplace transform of the given function f(t) = cos³ (t)?
3 S
3s
s² + 1
3 S
3√√π
4s5/2
C)
D)
C)
D)
D)
C)
D)
L{eat f(t)}: = F(s)eat
L{eat f(t)} = F(s-a)eat
f(t) = cos² (2t)?
1/1
S
- (+²+)
2
s² + 4.
4
s² + 16A
F(s) =
1/1
F(s) = +
2
(s-4)³
2
D)
4² (s + 1)
√√π
4(s+1) 5/2
7. Find the Laplace transform of f(t) = (1 + sin 2t cos 2t).
s² +2s + 16
s(s² + 16)
s²+2s + 16
(s² + 16)
C)
F(S)=3+
F(s) =
D)
F(s) =
F(s) =
2
53
F(s) =
F(s) =
(s² + 16)³
2s³96
(s² + 16)³
+
4 s² + 1
,then the Laplace transform of t³/²e-t is:
C)
3√√π
F(s)=5 (s + 1)
4s²
F(s) =
4s
s² +9
+
1 S
4 s² +9
3√π
4(s+1) 5/2
s²+2s +4
s(s² + 16)
s² + 2s + 16
s(s² + 4)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bae0010-3da3-459c-834e-8e5a4ca3ff4e%2F402696d2-0d39-4e3e-9860-304fc1efaea9%2F6f5ne9f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. If L{f(t)} = F(s), then
A)
L{eat f(t)} = F(s + a)
B) L{eat f(t)} = F(sa)
2. What is the Laplace transform of the given function
1/1
A) F(s) == +
S
2 s s² + 16A
1/1 S
B) F(S) = (²+4)
3. Given f(t) = e4t, what is L{t²f(t)}?
1
(s - 4)²
1
A)
B)
A) F(s) =
S3
2
B) F(S)=3
A)
B) F(s) =
F(s) =
(s - 4)²
(s-4)³
4. What is the Laplace transform of the given function f(t) = 2t² cos² (2t)?
2 2s³ - 96
2
1
A) F(S) = -5
A) F(S)
+
B) F(s) =-
=
B) F(s) =
s + 16
S² + 16
2s(s - 16)
s² + 16
S
4 s² +1
3s +1
4(s² +9)
6. If the Laplace transform of x³/² is
3√√π
+
4 s² +9
C)
D)
5. What is the Laplace transform of the given function f(t) = cos³ (t)?
3 S
3s
s² + 1
3 S
3√√π
4s5/2
C)
D)
C)
D)
D)
C)
D)
L{eat f(t)}: = F(s)eat
L{eat f(t)} = F(s-a)eat
f(t) = cos² (2t)?
1/1
S
- (+²+)
2
s² + 4.
4
s² + 16A
F(s) =
1/1
F(s) = +
2
(s-4)³
2
D)
4² (s + 1)
√√π
4(s+1) 5/2
7. Find the Laplace transform of f(t) = (1 + sin 2t cos 2t).
s² +2s + 16
s(s² + 16)
s²+2s + 16
(s² + 16)
C)
F(S)=3+
F(s) =
D)
F(s) =
F(s) =
2
53
F(s) =
F(s) =
(s² + 16)³
2s³96
(s² + 16)³
+
4 s² + 1
,then the Laplace transform of t³/²e-t is:
C)
3√√π
F(s)=5 (s + 1)
4s²
F(s) =
4s
s² +9
+
1 S
4 s² +9
3√π
4(s+1) 5/2
s²+2s +4
s(s² + 16)
s² + 2s + 16
s(s² + 4)
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