Problem 예제.

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$\mathcal{L}^{-1} \left[ \dfrac{1}{s^2+a^2} \right]$ 은 어느 것인가?

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$\dfrac{1}{a} \cos at$

$\sin at$

$\cos at$

$\dfrac{1}{a} \sin at$

Solution

$\mathcal{L}(\sin \omega t) = \dfrac{\omega}{s^2+\omega^2}$

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

Correct answer: 4