Problem 02 | Second Shifting Property of Laplace Transform

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Problem 01
Find the Laplace transform of   $g(t) = \begin{cases}{f(t - 2)^3 & t > 2 \\ 0 & t  

Solution 01
$\displaystyle \mathcal{L} \left\{ g(t) \right\} = e^{-as} F(s)$
 

$F(s) = \mathcal{L} (t^3)$   and   $a = 2$

$F(s) = \dfrac{3!}{s^{3 + 1}}$

$F(s) = \dfrac{6}{s^4}$
 

Thus,
$\displaystyle \mathcal{L} \left\{ g(t) \right\} = e^{-2s} \left( \dfrac{6}{s^4} \right)$

Problem 01 | Second Shifting Property of Laplace Transform

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Problem 01
Find the Laplace transform of   $g(t) = \begin{cases}{f(t - 1)^2 & t > 1 \\ 0 & t  

Solution 01

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