Find the inverse Laplace transform of s 2 − 4 s − 4 s 4...

klupko5HR

klupko5HR

Answered

2022-11-25

Find the inverse Laplace transform of s 2 4 s 4 s 4 + 8 s 2 + 16

Answer & Explanation

Kozuh5F7

Kozuh5F7

Expert

2022-11-26Added 9 answers

Note that
L 1 [ a s 2 + a 2 ] = sin a t
and
L 1 [ s 2 a 2 ( s 2 + a 2 ) 2 ] = t cos a t ,
then
a s 2 + a 2 a s 2 a 2 ( s 2 + a 2 ) 2 = 2 a 3 ( s 2 + a 2 ) 2 .
Hence
L 1 [ 2 a 3 ( s 2 + a 2 ) 2 ] = sin a t a t cos a t
and
L 1 [ 8 ( s 2 + 4 ) 2 ] = 1 2 ( sin 2 t 2 t cos 2 t ) .

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