Problem 예제.

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그림과 같은 구형파의 라플라스 변환은?

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$\dfrac{2}{s}(1-e^{4s})$

$\dfrac{4}{s}(1-e^{-2s})$

$\dfrac{4}{s}(1-e^{2s})$

$\dfrac{2}{s}(1-e^{-4s})$

Solution

$f(t) = 2 ( u(t) - u(t-4))$

$\mathcal{L}(f(t))=\mathcal{L}(2 ( u(t) - u(t-4))) = 2 \left( \dfrac{1}{s} - \dfrac{e^{-4s}}{s} \right) = \dfrac{2}{s} \left( 1 - e^{-4s} \right)$

Correct answer: 4