Given L(t^2)=(2)/(s^3) but why is is that, if we use the convolution theorem for 1 ** t^2, we get L(1 ** t^2)=1/s ** (2)/(s^3)

Lina Neal 2022-09-12 Answered
I know that
L ( t 2 ) = 2 s 3
but why is is that, if we use the convolution theorem for 1 t 2 , we get
L ( 1 t 2 ) = 1 s 2 s 3
Isn't 1 t 2 equal to t 2 ?
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Answers (1)

Maggie Tanner
Answered 2022-09-13 Author has 18 answers
L ( 1 t 2 ) = L ( 1 ) L ( t 2 ) = 1 s × 2 ! s 3 = 2 s 4
Note that the convolution theorem gives us :
f ( t ) = 1 t 2 = 0 t 1 × τ 2 d τ
f ( t ) = τ 3 3 | 0 t = t 3 3
L ( f ( t ) ) = 1 3 3 ! s 4 = 2 s 4

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