Page 55 - LAPLACE TRANSFORM
P. 55
Example 9
Find the Inverse Laplace Transform of the following.
6 +s 6
L 1 − { }
s 2 − 36
Refer to the expression , , so
− +
6s 6
= L 1 − { }+ { }
(s 2 − 36 s 2 − 36
s 6
= 6L 1 − { }+ L 1 − { }
s 2 − 36 s 2 − 36
= cosh6 6 t sinh t 6
−
Example 10
Find the Inverse Laplace Transform of the following.
s
( + ) 2
L − 1 {
s
2
( + ) 2 − 25
Refer to the expression + , so
( + ) −
−1
= { ( +2) }
2
( +2) −25
= −2 ℎ 5
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