3 cosh 2t 3s 2) -4
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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Find the Inverse Laplace Transforms of the following : Please solve problem number 2 only. Answer are already given on its side. Thanks!
![Inverse Laplace Transforms
Find the Inverse Laplace Transforms of the following.
Linearity
F(s)
f(t)
4et
F(s)
f(t)
4
1)
S-3
48 – 60V5
4)
32 %
8t°
6 cos 3t – 18 sin 3t
3s
2)
s? - 4
3s +3s
3)
3 cosh 2t
6s - 54
5)
s? +9
3s +9
6)
s? +5
9/5
-sin 5t
5
3 cos 5t +
8
Completing the Square and Translations
F(s)
10s +15
1)
s? – 2s +5
f(t)
F(s)
f(t)
25
10e' cos 2t +e' sin2t
4)
s? – 2s +9
e' sin2/2t
2
V2s
e% 5
+te %
2
VZe' cos Zt + e' sin žt
2)
s? – 2s + 3
4s+ 12
5)
4s? +4s+1
5.
V10
12s - 24
6)
s? +16
S+2
12cos4t – 6sin4t
3)
2s? + 4s + 7
cos,t+
10
sin,
Partial Fractions
f(t)
10(e-10t -e 201)
F(s)
100
1)
(s+10)(s+ 20)
s? - 2s +5
2)
(s-2)°
5
e + 2te" +t'et
4s +3
3)
(s– 1)(s² + 1)
7
7
-e'
t+-sint
- cost+-
2
5
sint-e sin2t
s? + 2s +7
1
4)
(s? +2s + 2)(s? + 2s+ 5)
2
e- cost + sint
5)
(s + 1)(s² +1)
2s + 42
6)
2s? – 7s - 15
4e – 3e %
4
1- cos 2t
7)
s(s² + 4)
2
e*- cost + sint
8)
(s+ 1)(s² +1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefad1d3d-95a1-469c-a887-1bb937f0b711%2F1439cd44-1eb9-435f-96f8-538458afc99e%2F68tw4ms_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Inverse Laplace Transforms
Find the Inverse Laplace Transforms of the following.
Linearity
F(s)
f(t)
4et
F(s)
f(t)
4
1)
S-3
48 – 60V5
4)
32 %
8t°
6 cos 3t – 18 sin 3t
3s
2)
s? - 4
3s +3s
3)
3 cosh 2t
6s - 54
5)
s? +9
3s +9
6)
s? +5
9/5
-sin 5t
5
3 cos 5t +
8
Completing the Square and Translations
F(s)
10s +15
1)
s? – 2s +5
f(t)
F(s)
f(t)
25
10e' cos 2t +e' sin2t
4)
s? – 2s +9
e' sin2/2t
2
V2s
e% 5
+te %
2
VZe' cos Zt + e' sin žt
2)
s? – 2s + 3
4s+ 12
5)
4s? +4s+1
5.
V10
12s - 24
6)
s? +16
S+2
12cos4t – 6sin4t
3)
2s? + 4s + 7
cos,t+
10
sin,
Partial Fractions
f(t)
10(e-10t -e 201)
F(s)
100
1)
(s+10)(s+ 20)
s? - 2s +5
2)
(s-2)°
5
e + 2te" +t'et
4s +3
3)
(s– 1)(s² + 1)
7
7
-e'
t+-sint
- cost+-
2
5
sint-e sin2t
s? + 2s +7
1
4)
(s? +2s + 2)(s? + 2s+ 5)
2
e- cost + sint
5)
(s + 1)(s² +1)
2s + 42
6)
2s? – 7s - 15
4e – 3e %
4
1- cos 2t
7)
s(s² + 4)
2
e*- cost + sint
8)
(s+ 1)(s² +1)
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