Page 36 - LAPLACE TRANSFORM

Example 6

By using the First Shifting Theorem determine the Laplace Transforms.

f ) (t = L {e 3t cos 2 2t }

1 s
we know that :- {cos 2 2t } = +
L
2s 2s 2 + 32
1 s
L {cos 2 2t } = +
2s 2s 2 + 32
1 ( − ) 2
s
L {e 2t cos 2 2t } = +
s
s
2
( 2 − ) 2 ( 2 − ) 2 + 32
s
1 ( − ) 2
= +
s
2 − 4 ( 2 − 2 s ) 2 + 32
)( −
s
s
1 ( − ) 2
= 2 − 4 + ( 2 s 2 − 2 − ss 2 + ) 4 + 32
s
s
1 ( − ) 2
= +
4 +
2 − 4 ( 2 s 2 − s ) 4 + 32
s
s
1 ( − ) 2
= +
8 +
2 − 4 2s 2 − s 8+ 32
s
s
1 ( − ) 2
= +
8 +
s
2 − 4 2s 2 − s 40

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