Page 65 - LAPLACE TRANSFORM
P. 65
Solution
dx
– 4x = 8
dt
x’ – 4x = 8
8
{s X(s) – x (0)} – 4X(s) =
s
8
{s X(s) – 2} – 4X(s) =
s
8
X(s) (s – 4) = + 2
s
s
8
X(s) (s – 4) = + 2 .
s s
8
2s
X(s) (s – 4) = +
s s
X(s) (s – 4) = 8 + 2s
s
A
X(s) = 8 + 2s = + B
s (s−4) s (s−4)
8 + 2s = A ( − ) + Bs
when s = 0; + = ( − ) +
8 + 2(0) = A (0 − 4)
8 = −4A
A = = −
−
when (s − 4) = 0
s= 4; 8 + 2s = A ( − ) + Bs
8 + 2s = B s
8 + 2(4) = B(4)
16 = 4B
B = =
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