282 -35 - 2 Y(s) z(1 + s)s

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 60RE
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Given the function
-282 - 35 - 2
Y(s)
s(s + 1)2
1. Use Partial Fractions to break apart the large fraction into smaller fractions
2. Then use the Laplace Transform table to convert these smaller fractions into f(t).
f(t)
Y(s)
%3D
S - A
N!
B
sinl R
s2 + B
cos( B t)
52
+ B2
N!
(s - A)N+1
B
Al sin(B t)
(s - A)? + B?
5 - A
A' cos( B 1)
(s - A)? + B2
A s(1) - -2 + te
B s(1) - -3+ e
© s(1) -e" sin(21)
D s() - -21 + 1
Os(1) - -2 cos(t)
Transcribed Image Text:Given the function -282 - 35 - 2 Y(s) s(s + 1)2 1. Use Partial Fractions to break apart the large fraction into smaller fractions 2. Then use the Laplace Transform table to convert these smaller fractions into f(t). f(t) Y(s) %3D S - A N! B sinl R s2 + B cos( B t) 52 + B2 N! (s - A)N+1 B Al sin(B t) (s - A)? + B? 5 - A A' cos( B 1) (s - A)? + B2 A s(1) - -2 + te B s(1) - -3+ e © s(1) -e" sin(21) D s() - -21 + 1 Os(1) - -2 cos(t)
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