t< 3 4 5. g(t) = e(t-3) t23
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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Find the Laplace transform of each of the following functions and simplify the result. Problem no. 5 only. Thanks!
Transcribed Image Text:Exercises
Find the Laplace transform of each of the following functions and simplify the result.
2a
F(s) =
1. f(t) = 2(1–e")
s(S+a)
(6s – 48)
F(s) =
s? +4s +40
2. f(t) = 2eª(3cos6t – 5sin6t)
12
F(s) =
(s+4)*
%3D
3. f(t) = 2t'e"
2e %
F(s) =
(s+3)%
4. f(t) =
Го
4
et-3)
-3s
t<3
G(s) =
(s-1)
5. g(t) =
t23
cos 2 t- t2
se
G(s) =
(s² + 4)
6. g(t) :
4e 6*
G(s) =
t<5
t25
7. g(t) = [(t-5)²
(s-2)
G(s) =
(s- 2)² +1 (s-2)² + 49_
(s-2)
8. g(t) = 2e"sin4tsin3t
3e% sin3tsinh 7t
4.5
4.5
H(s) =
(s – 6.5)² +9 (s+7.5)² +9
j2
H(s) =
s(s- 4)
9. h(t) =
10. h(t) = e"sinj2t
Product Identities
sin(A +B)+ sin(A –B)
sinA cosB
1.
sin(A +B)- sin(A -B)
cos A sinB
2.
cos(A -B)+ cos(A+B)
cos A cosB:
3.
2
cos(A -B)- cos(A+B)
sinA sinB
4.
Transcribed Image Text:Table of Laplace and Inverse Laplace Transforms
Time Domain
Complex Frequency Domain
F(s) = L f(t)
Functions
f(t)
Ø(t)
H(t)
Unit Impulse
1
Unit Step (Heaviside)
1/s
e "/s
Vs?
H(t-a)
-as
Unit Ramp
n!
Polynomial
sit
4s
t12)
pla-X (n=1,2..)
(1)(3)(5)....(2n – 1)/ (-)
2"
1
(s'k)
Exponential
e
kth Order
Exponential
n!
t'e
(s'k)""
Sine Wave
sin bt
s +b
Cosine Wave
cos bt
s +b
sinh bt
s -b
cosh bt
-b'
Damped Sine Wave
e" sinbt
(s'k}° +b²
Damped Cosine
Wave
(s`k)
(s kỷ +b²
" cosbt
b
' sinhbt
(s k)' -b"
(s`k)
(s`k -b?
e" coshbt
2bs
t sin bt
(s² +b² y°
(s² –b²)
(s² +b³ }°
2b
(s² +b° °
t cos bt
sin bt – bt cosbt
- 10 -
1030
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