Problem 예제.

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$f(t) = \cos^2 t$ 인 함수의 라플라스 변환을 구하면?

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$\dfrac{1}{2s}+\dfrac{s}{2(s^2+4)}$

$\dfrac{s}{2(s^2+4)}-\dfrac{1}{2s}$

$\dfrac{1}{s^2}+\dfrac{4}{s}$

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

Solution

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

$\mathcal{L} (\cos^2 t) = \mathcal{L}\left( \dfrac{1}{2} (1 + cos 2t) \right) = \dfrac{1}{2} \left( \dfrac{1}{s}+ \dfrac{s}{s^2+4} \right)$

Correct answer: 1