Find the inverse transform of the given functions: 3s2+5s+5 1. F(s): (s3+8s2+19s+12)(s³) 2. F(s): 5s+3 6S 8 -6 - (5s²+4s+1) s2+7
Find the inverse transform of the given functions: 3s2+5s+5 1. F(s): (s3+8s2+19s+12)(s³) 2. F(s): 5s+3 6S 8 -6 - (5s²+4s+1) s2+7
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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Transcribed Image Text:Table of Laplace Transforms
f(1) = L ' {F(s)}
F (s) = L{f(t)}
f(1) = L" {F(s)}
F(s) = L{f(t)}
1
1
1
2.
at
1.
S
S - a
п!
Г(р+1)
t", n=1,2,3,...
4.
t° ,p > -1
sn+1
sP+l
1-3-5...(2n – 1) VT
6. t" , n=1,2,3,...
3
2s?
2" s"+}
a
sin (at)
8. cos(at)
7.
s? +a?
s? + a?
2as
s² – a?
i sin (at)
10. i cos (at)
9.
(s² +a* }
(s° +a*)
2
2a
2as?
11. sin (at) - at cos (at)
sin (at) + at cos (at)
12.
(s° +a*}
(s²
s(s² - a° )
(s° +a*)°
+a
s(s² + 3a*)
За?)
13. cos(at)- at sin(at)
14. cos (at)+ at sin (at)
+a
s sin (b)+a cos (b)
s cos (b)-a sin(b)
15. sin (at +
b)
16. cos (at + b)
s? + a?
s' +a
S
17.
sinh (at)
18. cosh(at)
s² – a?
s² - a?
S - a
19.
e“ sin (bt)
20.
e“ cos (bt)
2
(s-a) +b?
(s - a)* +
+b?
S - a
e" sinh (bt
21.
(ы)
e" cosh (bt)
22.
(s – a)' – b²
(s - a)' –b?
n!
23. 1"е", п %3D1,2,3,...
24. f(ct)
1
-F
n+1
(s -a)**
C
u.(1) =u (t -c)
25.
8 (t-c)
CS
26.
CS
e
Heaviside Function
S
Dirac Delta Function
27. и. (1)/ (г—с)
29. e“ f (t)
)
F(s-c)
u.(t)g (t)
t" f (t), n=1,2,3,...
e "L{g(t+c}}
(-1)" F (s)
F(s)
+1) ¿
(n)
CS
e *F (s
28. и.
C
1
31. f(1)
| F(u) du
32. f(v)dv
S
T
-st
33. f (1-t)g(T)dt
F(s)G(s)
34. f(t+T)= f(t)
e " f (t) dt
-sT
1-e
s³F(s)- sf (0)-f'(0)
sF (s)- f (0)
s"F(s)– s*\f(0)-s*-²f"(0)..-- sf(=-³ (0)– fla-) (0)
35. f'(t)
36. f"(t)
37. f (t)
3.
5.
Transcribed Image Text:Find the inverse transform of the given functions:
3s2+5s+5
1. F(s) :
(s³+8s²+19s+12)(s³)
5s+3
6s
8
2. F(s)
9-
(5s²+4s+1)
s2+7
Evaluate using Laplace Transform:
f (t) = .
tcos 3t
dt
e-4t
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