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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
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 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)
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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