2. Inverse Laplace Transform Find the inverse Laplace transform of the following functions (a). F(s) = 2+35-4 s²+3s-4 2 2 1 1 F(s) = = = (s - 4) (s + 1) S- 4 s+1 2s+4 (b). F(s) = s²+2s+5€ -2s f(t) = (e" - e'). 2s +4 s²+2s+5 whose inverse Laplace transform is -t 2(s+1)+2 = (s+1)²+22 2e cos(2t) + et sin(2t) By checking the table, f(t) is the shifted version of this function. f(t)=(2e (2) cos(2(t − 2)) + e-(-2) sin(2(t − 2)))u2(t).
2. Inverse Laplace Transform Find the inverse Laplace transform of the following functions (a). F(s) = 2+35-4 s²+3s-4 2 2 1 1 F(s) = = = (s - 4) (s + 1) S- 4 s+1 2s+4 (b). F(s) = s²+2s+5€ -2s f(t) = (e" - e'). 2s +4 s²+2s+5 whose inverse Laplace transform is -t 2(s+1)+2 = (s+1)²+22 2e cos(2t) + et sin(2t) By checking the table, f(t) is the shifted version of this function. f(t)=(2e (2) cos(2(t − 2)) + e-(-2) sin(2(t − 2)))u2(t).
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:2. Inverse Laplace Transform
Find the inverse Laplace transform of the following functions
(a). F(s) = 2+35-4
s²+3s-4
2
2
1
1
F(s) =
=
=
(s - 4) (s + 1)
S-
4
s+1
2s+4
(b). F(s) = s²+2s+5€
-2s
f(t) = (e" - e').
2s +4
s²+2s+5
whose inverse Laplace transform is
-t
2(s+1)+2
=
(s+1)²+22
2e cos(2t) + et sin(2t)
By checking the table, f(t) is the shifted version of this function.
f(t)=(2e (2) cos(2(t − 2)) + e-(-2) sin(2(t − 2)))u2(t).
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