1. P(s) = 10 2. F(s) 572 S г 5+25 3. F(S) = + ㅗ 35-5 3 5²425 8 3 + 35²+12 5²49 Ale

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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Advance Engineering Math. Topic: Inverse Laplace using table. Pls show clean and full solution tnx.
← Laplace_Table.pdf E
1.
3.
5.
7.
9.
f(t)=2-¹{F(s)}
1
t", n=1,2,3,...
√t
sin (at)
t sin(at)
11. sin(at)-at cos (at)
13. cos(at)-at sin(at)
15. sin(a+b)
17. sinh(at)
19. e sin (br)
21. e" sinh(bt)
23. tet, n=1,2,3,...
u(t)= u(t-c)
Heaviside Function
25.
27. u. (t)f(t-c)
29. e f(t)
31.
ƒ(1)
33. (1-1)g (1) dr
35. f'(t)
37. f(") (1)
Table of Laplace Transforms
F(s) = £{f(t)}
1
n!
S+1
√√π
2st
a
s² + a²
2as
(s² + a²)²
2a³
(s² + a²)²
s(s²-a²)
(s² + a²)²
s sin (b) + acos (b)
s² + a²
a
s²-a²
b
(s-a)² + b²
b
(s-a)²-b²
n!
(s-a)"
ees
S
e-F(s)
F(s-c)
F(u) du
2.
f(t)=L-¹{F(s)}
eªr
4. t,p>-1
6. t", n=1,2,3,...
8. cos (at)
10. tcos(at)
12. sin (at) + at cos (at)
14. cos(at)+ at sin (at)
16. cos(at+b)
18. cosh (at)
20. e" cos (bt)
22. e cosh (bt)
24. f(ct)
(t-c)
Dirac Delta Function
26.
28. u(t)g(1)
30. tf(t), n=1,2,3,...
32. ff(v) dv
F(s)G(s)
SF (s)-f(0) 36. f"(t)
34. f(t+T)=f(t)
F(s)=L{f(t)}
1
s-a
r(p+1)
SP+1
1.3.5...(2n-1)√√
2" **
S
s² + a²
s²-a²
(s² + a²)²
2as²
(s² + a²)²
s(s² +3a²)
(s² + a²)²³
scos (b)-asin (b)
s² + a²
S
s²-a²
s-a
(s-a)² + b²
s-a
(s-a)²-b²
+0
e™
e¯"L{g(t+c)}
(-1)" F) (s)
F(s)
S
fef(t) dt
1-es
s²F(s)-sf (0)-f'(0)
s" F (s)-s"-f(0)-s"²f'(0)-sf)(0)-f(-¹)(0)
:
Transcribed Image Text:← Laplace_Table.pdf E 1. 3. 5. 7. 9. f(t)=2-¹{F(s)} 1 t", n=1,2,3,... √t sin (at) t sin(at) 11. sin(at)-at cos (at) 13. cos(at)-at sin(at) 15. sin(a+b) 17. sinh(at) 19. e sin (br) 21. e" sinh(bt) 23. tet, n=1,2,3,... u(t)= u(t-c) Heaviside Function 25. 27. u. (t)f(t-c) 29. e f(t) 31. ƒ(1) 33. (1-1)g (1) dr 35. f'(t) 37. f(") (1) Table of Laplace Transforms F(s) = £{f(t)} 1 n! S+1 √√π 2st a s² + a² 2as (s² + a²)² 2a³ (s² + a²)² s(s²-a²) (s² + a²)² s sin (b) + acos (b) s² + a² a s²-a² b (s-a)² + b² b (s-a)²-b² n! (s-a)" ees S e-F(s) F(s-c) F(u) du 2. f(t)=L-¹{F(s)} eªr 4. t,p>-1 6. t", n=1,2,3,... 8. cos (at) 10. tcos(at) 12. sin (at) + at cos (at) 14. cos(at)+ at sin (at) 16. cos(at+b) 18. cosh (at) 20. e" cos (bt) 22. e cosh (bt) 24. f(ct) (t-c) Dirac Delta Function 26. 28. u(t)g(1) 30. tf(t), n=1,2,3,... 32. ff(v) dv F(s)G(s) SF (s)-f(0) 36. f"(t) 34. f(t+T)=f(t) F(s)=L{f(t)} 1 s-a r(p+1) SP+1 1.3.5...(2n-1)√√ 2" ** S s² + a² s²-a² (s² + a²)² 2as² (s² + a²)² s(s² +3a²) (s² + a²)²³ scos (b)-asin (b) s² + a² S s²-a² s-a (s-a)² + b² s-a (s-a)²-b² +0 e™ e¯"L{g(t+c)} (-1)" F) (s) F(s) S fef(t) dt 1-es s²F(s)-sf (0)-f'(0) s" F (s)-s"-f(0)-s"²f'(0)-sf)(0)-f(-¹)(0) :
1. P(s) = 10
2. F(s)
572
3. F(5)=
S
v
5+25
35²x12
f
ㅗ
35-5
3
5425
+
3
5²49
+
7
Transcribed Image Text:1. P(s) = 10 2. F(s) 572 3. F(5)= S v 5+25 35²x12 f ㅗ 35-5 3 5425 + 3 5²49 + 7
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