Problem 예제.

Multiple Choice • Views 729 • Comments 1 • Last Updated at 1 month ago

다음 함수 $F(s) = \dfrac{5s+3}{s(s+1)}$ 의 역라플라스 변환은 어떻게 되는가?

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$3-2e^{-t}$

$2+3e^{-t}$

$3+2e^{-t}$

$2-3e^{-t}$

Solution

$\dfrac{5s+3}{s(s+1)} = \dfrac{k_1}{s} + \dfrac{k_2}{s+1}$

$k_1 = \lim_{s \to 0} s\left[ \dfrac{5s+3}{s(s+1)} \right] = 3$

$k_2 = \lim_{s \to -1} (s+1)\left[ \dfrac{5s+3}{s(s+1)} \right] = 2$

$\mathcal{L}^{-1} \left[ \dfrac{3}{s} + \dfrac{2}{s+1} \right] = 3 + 2e^{-t}$

Correct answer: 3