Page 60 - LAPLACE TRANSFORM

when s= 2;
2
10s + 4 = A(s + 4) + (Bs + C) { ( − 2) }
2
10(2) + 4 = A( 2 + 4 )
24 = 8

= =

2
10s + 4 = A(s + 4) + (Bs + C) { ( − 2) }
2
2
10s + 4 = As + 4A + Bs − 2 + − 2C

2
s ; 0 = A + B ............................... (1)
1
s ; 10 = −2B + C ........................ (2)
0
s (without s); 4 = 4A −2C ........................... (3)

0 = A + B .............................. (1)
B = −A = −

10 = −2B + C ..................... (2)

C = 10 + 2B
C = 10 + 2(−3)

C = 4

f(t) = + +
2
−2 s +4

= 3 + −3 +4
2
−2 s +2 2

1 3 −4
= 3 { } − { }
2
−2 s +2 2

2t
= 3 e − { 3 − 4 }
2
2
s +2 2 s +2 2

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