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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Question
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Advance Engineering Math.
Topic: Inverse Laplace using table.
Pls show clean and full solution tnx.
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)
:
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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