Problem 예제.

Multiple Choice • Views 714 • Comments 1 • Last Updated at 1 month ago

$F(s) = \dfrac{s+1}{s^2+2s}$ 로 주어졌을 때 의 역변환을 한 것은?

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$\dfrac{1}{2}(1+e^{-2t})$

$\dfrac{1}{2}(1+e^t)$

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

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

Solution

$\dfrac{s+1}{s^2+2s} = \dfrac{k_1}{s} + \dfrac{k_2}{s+2}$

$k_1 = \lim_{s \to 0} s\left[ \dfrac{s+1}{s(s+2)} \right] = 0.5$

$k_2 = \lim_{s \to -2} (s+2)\left[ \dfrac{s+1}{s(s+2)} \right] = 0.5$

$\mathcal{L}^{-1} \left[ \dfrac{0.5}{s} + \dfrac{0.5}{s+2} \right] = 0.5 + 0.5e^{-2t}$

Correct answer: 1