Page 68 - LAPLACE TRANSFORM

Solution

3t
5 ′ – 20x = 30e
30
5{sX(S) − x(0)} − 20X(S) =
(s−3)
30
5{sX(S) – 2} − 20X(S) =
(s−3)
30
5sX(S) – 10 − 20X(S) =
(s−3)
30
X(S) {5s – 20} − 10 =
(s−3)
30
X(S) {5s – 20} = + 10
(s−3)

X(S) {5s – 20} = 30 + 10 (s−3)
(s−3) (s−3)

X(S) {5s – 20} = 30 + 10 (s−3)
(s−3)
30 + 10 (s−3)
X(S) =

(s−3) (5 −20)
30 + 10 (s−3)
X(S) =

(s−3) .5( −4)
X(S) = 6 + 2 (s−3)

(s−3) ( −4)
6 + 2s−6
X(S) =

(s−3) ( −4)
2s A B
X(S) = = +

(s−3) ( −4) (s−3) (s − 4)

multiply each side with (s − 3)(s − 4)

X(S) = 2s(s−3)(s−4) = A(s−3)(s−4) + B(s−3)(s−4)

(s−3) ( −4) (s−3) (s − 4)
2s = A(s − 4) + B(s − 3)

when s = 3 2s = A(s − 4) + B(s − 3)

2(3) = A(3 − 4)

6 = −A

A = −

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