Page 89 - LAPLACE TRANSFORM
P. 89
By applying the Laplace transform method;
1 10
L [sI(s) − i(0)] + [I(s) + q0] =
CS S−2
By assuming zero initial condition;
1 10
L [sI(s)] + [ I(s)] =
CS S−2
I(s) 10
5sI(s) + =
. S−2
50I(s) 10
5sI(s) + =
S−2
10
I(s)[ 5s + ] =
S−2
2
5s +50 10
I(s) { } =
s S−2
I(s) = 10 x s
2
(s − 2) (5s + 50)
I(s) = 10s = 10s = 2s
2
2
2
(s − 2)(5s + 50) (s − 2). 5(s + 10) (s − 2)(s + 10)
I(s) = 2s = A + (Bs+C)
2
2
(s − 2)(s + 10) (s − 2) (s + 10)
2s = A( + ) + (Bs + C) (s – 2)
when s=2 ;2s = A( + ) + (Bs + C) (s – 2)
2
2(2) = A [(2) + 10]
4 = A [14]
A = =
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