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人気のある微分積分 >

laplacetransform e^{-3t}*sin(t)

解

ラプラス変換

e^{- 3 t} \cdot sin (t)

解

\frac{1}{( s + 3 ) ^{2} + 1}

解答ステップ

L {e^{- 3 t} sin (t)}

変換ルールを適用:

L {f (t)} = F (s)

ならば

L {e^{a t} f (t)} = F (s - a)

e^{- 3 t} sin (t)

向け

: f (t) = sin (t), a = - 3

= L {sin (t)} (s + 3)

L {sin (t)} : \frac{1}{s ^{2} + 1}

= \frac{1}{( s + 3 ) ^{2} + 1}

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