ADVANCED ENGINEERING MATHEMATICS 9. cosh at cos at 1028 7. e-2 sin 4t 10. e-3 (2 cos 5t - 3 sin 5t) 12. et (sin 2t2t cos 2t) 15. If L (ft)) = f(s), show that L 8. 13-3 11. sin at - - at cos at 13. sinh - sin - {(음)}- af (as). √√√3 t 2 16. Show that L (sin kê sinh k} = 2k2s s4 + 4k⭑ 17. Show that 2as (i) Lit sin at} = (ii) Llt cos at) = (s² + a2)² (s² + a2)² 18. Find the Laplace transform of fit) defined as (i) ft)=5, St. 0 4 (iii) ft) = (cost, 10, 02 (ii) ft)= {0. [sin t, (iv) fit) = 2 -1 7, 0R 0 3. ft)|t1|+ Find the Laplace transform of fit) defined as 19. [Hi 2, Hint. f(t) = -{3/4 05111] 14. t eat sin at +11, t≥0. 1. 2a2 $4 3. Answers 2. s cos b- a sin b Zabs [s² + (a+b)2][s² + (a - b)2] 48 6. - 4) (s2 -36) s-a s+a 9. 12. 18. (z) +e + +a2 (s+a)2 + a 2 (s- a)² + a 16 (s² + 2s + 5)² (-) 18 4. s(s² + 36) 4 7. s2 +45 + 20 2s-9 10. 2 32+ 6s+34 13. √√√3 s 2(s +82 +1) 5. 8. 11. s(s2 +28) (s² + 4)s2 + 36) 6 (s+3) 2a3 (s² + a2)² 14. (s 2a(sa) - 2as + 2a) (ii) 1+6~ 2+1 (iii) s(1-e-2) +1 -2s (iv) (2 + 3s + 382) + e-3a 2 (5s-1) 19. S
ADVANCED ENGINEERING MATHEMATICS 9. cosh at cos at 1028 7. e-2 sin 4t 10. e-3 (2 cos 5t - 3 sin 5t) 12. et (sin 2t2t cos 2t) 15. If L (ft)) = f(s), show that L 8. 13-3 11. sin at - - at cos at 13. sinh - sin - {(음)}- af (as). √√√3 t 2 16. Show that L (sin kê sinh k} = 2k2s s4 + 4k⭑ 17. Show that 2as (i) Lit sin at} = (ii) Llt cos at) = (s² + a2)² (s² + a2)² 18. Find the Laplace transform of fit) defined as (i) ft)=5, St. 0 4 (iii) ft) = (cost, 10, 02 (ii) ft)= {0. [sin t, (iv) fit) = 2 -1 7, 0R 0 3. ft)|t1|+ Find the Laplace transform of fit) defined as 19. [Hi 2, Hint. f(t) = -{3/4 05111] 14. t eat sin at +11, t≥0. 1. 2a2 $4 3. Answers 2. s cos b- a sin b Zabs [s² + (a+b)2][s² + (a - b)2] 48 6. - 4) (s2 -36) s-a s+a 9. 12. 18. (z) +e + +a2 (s+a)2 + a 2 (s- a)² + a 16 (s² + 2s + 5)² (-) 18 4. s(s² + 36) 4 7. s2 +45 + 20 2s-9 10. 2 32+ 6s+34 13. √√√3 s 2(s +82 +1) 5. 8. 11. s(s2 +28) (s² + 4)s2 + 36) 6 (s+3) 2a3 (s² + a2)² 14. (s 2a(sa) - 2as + 2a) (ii) 1+6~ 2+1 (iii) s(1-e-2) +1 -2s (iv) (2 + 3s + 382) + e-3a 2 (5s-1) 19. S
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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Answer no. 19 only
![ADVANCED ENGINEERING MATHEMATICS
9. cosh at cos at
1028
7.
e-2 sin 4t
10.
e-3 (2 cos 5t - 3 sin 5t)
12.
et (sin 2t2t cos 2t)
15.
If L (ft)) = f(s), show that L
8. 13-3
11. sin at - - at cos at
13. sinh - sin
- {(음)}-
af (as).
√√√3 t
2
16.
Show that L (sin kê sinh k} =
2k2s
s4 + 4k⭑
17.
Show that
2as
(i) Lit sin at} =
(ii) Llt cos at) =
(s² + a2)²
(s² + a2)²
18.
Find the Laplace transform of fit) defined as
(i) ft)=5,
St.
0<t<4
t> 4
(iii) ft) =
(cost,
10,
0<t<2
t>2
(ii) ft)= {0.
[sin t,
(iv) fit) =
2
-1
7,
0<t<x
t>R
0<t<2
2<t<3
t> 3.
ft)|t1|+
Find the Laplace transform of fit) defined as
19.
[Hi
2,
Hint. f(t) = -{3/4 05111]
14. t eat sin at
+11, t≥0.
1.
2a2
$4
3.
Answers
2.
s cos b- a sin b
Zabs
[s² + (a+b)2][s² + (a - b)2]
48
6.
-
4) (s2
-36)
s-a
s+a
9.
12.
18.
(z)
+e
+
+a2 (s+a)2 + a
2 (s- a)² + a
16
(s² + 2s + 5)²
(-)
18
4.
s(s² + 36)
4
7.
s2 +45 + 20
2s-9
10.
2
32+ 6s+34
13.
√√√3 s
2(s +82 +1)
5.
8.
11.
s(s2
+28)
(s² + 4)s2 + 36)
6
(s+3)
2a3
(s² + a2)²
14. (s
2a(sa)
- 2as + 2a)
(ii)
1+6~
2+1
(iii)
s(1-e-2)
+1
-2s
(iv)
(2 + 3s + 382) +
e-3a
2
(5s-1)
19.
S](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbe770e3-285b-4d19-8f35-3df6db5ded2d%2F0583608c-c444-4a8d-a49f-589233ca3ffd%2Fg3tjrwm_processed.png&w=3840&q=75)
Transcribed Image Text:ADVANCED ENGINEERING MATHEMATICS
9. cosh at cos at
1028
7.
e-2 sin 4t
10.
e-3 (2 cos 5t - 3 sin 5t)
12.
et (sin 2t2t cos 2t)
15.
If L (ft)) = f(s), show that L
8. 13-3
11. sin at - - at cos at
13. sinh - sin
- {(음)}-
af (as).
√√√3 t
2
16.
Show that L (sin kê sinh k} =
2k2s
s4 + 4k⭑
17.
Show that
2as
(i) Lit sin at} =
(ii) Llt cos at) =
(s² + a2)²
(s² + a2)²
18.
Find the Laplace transform of fit) defined as
(i) ft)=5,
St.
0<t<4
t> 4
(iii) ft) =
(cost,
10,
0<t<2
t>2
(ii) ft)= {0.
[sin t,
(iv) fit) =
2
-1
7,
0<t<x
t>R
0<t<2
2<t<3
t> 3.
ft)|t1|+
Find the Laplace transform of fit) defined as
19.
[Hi
2,
Hint. f(t) = -{3/4 05111]
14. t eat sin at
+11, t≥0.
1.
2a2
$4
3.
Answers
2.
s cos b- a sin b
Zabs
[s² + (a+b)2][s² + (a - b)2]
48
6.
-
4) (s2
-36)
s-a
s+a
9.
12.
18.
(z)
+e
+
+a2 (s+a)2 + a
2 (s- a)² + a
16
(s² + 2s + 5)²
(-)
18
4.
s(s² + 36)
4
7.
s2 +45 + 20
2s-9
10.
2
32+ 6s+34
13.
√√√3 s
2(s +82 +1)
5.
8.
11.
s(s2
+28)
(s² + 4)s2 + 36)
6
(s+3)
2a3
(s² + a2)²
14. (s
2a(sa)
- 2as + 2a)
(ii)
1+6~
2+1
(iii)
s(1-e-2)
+1
-2s
(iv)
(2 + 3s + 382) +
e-3a
2
(5s-1)
19.
S
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