Page 26 - LAPLACE TRANSFORM

Example 6

Find Laplace Transform, F(s) of given functions.

f t) ( = cos 2 t 2

By using the trigonometric identities

2
cos 2 = 2 cos A − 1
A

So
cos 2 =t 2 cos t − 1
2

cos t 4 = 2 cos 2 2 −
t 1
cos 4 t 1=+ 2 cos 2 t 2
t 1
cos 4 + = cos 2 2 t @ 1 cos t 4 + 1 = cos 2 t 2
2 2 2

So

1 1
cos 2 2t = + cos 4t
2 2
∴ { L 1 }+ 1 L {cos 4t }
2 2

1 1 s
= [ ]+ [ ]
2s 2 s 2 + 4 2
1 s
= +
2s 2s 2 + 32

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