Problem 예제.

Multiple Choice • Views 661 • Comments 1 • Last Updated at 1 month ago

라플라스 변환함수 $F(s) = \dfrac{s+2}{s^2+4s+13}$ 에 대한 역변환 함수 $f(t)$ 는?

Subscribe to see the correct answer.

$e^{2t}\sin 3t$

$e^{-3t}\cos 2t$

$e^{-2t}\cos 3t$

$e^{3t}\cos 2t$

Solution

$\mathcal{L} (e^{-at}\cos (\omega t))= \dfrac{(s+a)}{(s+a)^2+\omega^2}$

$\dfrac{s+2}{s^2+4s+13}= \dfrac{s+2}{s^2+4s+4+9}=\dfrac{s+2}{(s+2)^2+3^3}$

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

Correct answer: 3