Problem 예제.

Multiple Choice • Views 685 • Comments 0 • Last Updated at 1 month ago

$f(t)=\mathcal{L}^{-1} \left[ \dfrac{s^2+3s+10}{s^2+2s+5} \right]$ 는?

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$\delta(t) + e^{-t}(\cos 2t +2 \sin 2t)$

$\delta(t) + e^{-t}(\cos 2t - 2\sin 2t)$

$\delta(t) + e^{-t}(\cos 2t + \sin 2t)$

$\delta(t) + e^{-t}(\cos 2t - \sin 2t)$

Solution

$f(t) = \dfrac{s^2+3s+10}{s^2+2s+5} = \dfrac{s^2+2s+5 + s + 5}{s^2+2s+5}= 1+ \dfrac{s + 1}{(s+1)^2+2^2}+ 2 \dfrac{2}{(s+1)^2+2^2}$

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

Correct answer: 1