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라플라스 변환

라플라스 변환

$e^{-2t}\cos 3t$ 의 라플라스 변환은?

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1

$\dfrac{s}{(s-2)^2+3^2}$

2

$\dfrac{s}{(s+2)^2+3^2}$

3

$\dfrac{s-2}{(s-2)^2+3^2}$

4

$\dfrac{s+2}{(s+2)^2+3^2}$

Solution

$\mathcal{L} \left( e^{-at} f(t) \right) = F(s+a) \quad 이므로 \quad \mathcal{L} \left( e^{-2t} \cos(3t) \right) = \dfrac{s+2}{(s+2)^2+9}$

Correct answer: 4

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