Inverse Laplace Transforms Find the Inverse Laplace Transforms of the followin Linearity F(s) f(t) F(s 4. 4e 4) S-3 3s 2) -4 3 cosh 2t 5) 3s +3s 6) 8. Completing the Square and Translations F(s) f(t)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Inverse Laplace Transforms
Find the Inverse Laplace Transforms of the following.
Linearity
F(s)
f(t)
F(s)
f(t)
48-60/5
4)
8r - 32J%
4e
s-3
3s
2)
s-4
6s - 54
5)
s? +9
3 cosh 2t
6 cos 3t – 18sin3t
3s +3s
3s +9
6)
s' +5
3 cos 5t + 9V5
sin 5t
Completing the Square and Translations
F(s)
f(t)
F(s)
f(t)
10s +15
25
e' sin 2t
2
10e' cos 2t +
4)
s? – 2s +9
-e' sin2/2t
s- 2s +5
V2s
2)
s? - 2s +3
4s+12
5)
4s? +4s+1
V2e' cos 2t +e' sin /2t
V10
e sin
10
12s - 24
6)
s? +16
S+2
ecos.
2s² + 4s+7
12 cos 4t -6 sin 4t
Partial Fractions
F(s)
f(t)
100
/ 1)
(s+10)(s+20)
10(e-10t -e 20t)
s?- 2s +5
2)
(s-2)
e2 +2te2t +
4s+3
7.
7
1
sint
-e'
cost+
(s-1)(s? +1)
2
2
s? +2s +7
4)
(s? +2s+2)(s? +2s+5)
5
e sint--e' sin 2t
3
2
e - cost+ sint
(s+1)(s +1)
2s+42
6)
2s? – 7s-15
4e5t - 3e %
4.
s(s' +4)
1- cos 2t
8)
(s+1)(s² +1)
e- cost+sint
- 11 -
10
Transcribed Image Text:Inverse Laplace Transforms Find the Inverse Laplace Transforms of the following. Linearity F(s) f(t) F(s) f(t) 48-60/5 4) 8r - 32J% 4e s-3 3s 2) s-4 6s - 54 5) s? +9 3 cosh 2t 6 cos 3t – 18sin3t 3s +3s 3s +9 6) s' +5 3 cos 5t + 9V5 sin 5t Completing the Square and Translations F(s) f(t) F(s) f(t) 10s +15 25 e' sin 2t 2 10e' cos 2t + 4) s? – 2s +9 -e' sin2/2t s- 2s +5 V2s 2) s? - 2s +3 4s+12 5) 4s? +4s+1 V2e' cos 2t +e' sin /2t V10 e sin 10 12s - 24 6) s? +16 S+2 ecos. 2s² + 4s+7 12 cos 4t -6 sin 4t Partial Fractions F(s) f(t) 100 / 1) (s+10)(s+20) 10(e-10t -e 20t) s?- 2s +5 2) (s-2) e2 +2te2t + 4s+3 7. 7 1 sint -e' cost+ (s-1)(s? +1) 2 2 s? +2s +7 4) (s? +2s+2)(s? +2s+5) 5 e sint--e' sin 2t 3 2 e - cost+ sint (s+1)(s +1) 2s+42 6) 2s? – 7s-15 4e5t - 3e % 4. s(s' +4) 1- cos 2t 8) (s+1)(s² +1) e- cost+sint - 11 - 10
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