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人気のある微分積分 >

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

解

ラプラス変換

e^{- t} sin (3 t)

解

\frac{3}{( s + 1 ) ^{2} + 9}

解答ステップ

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

向け

: f (t) = sin (3 t), a = - 1

= L {sin (3 t)} (s + 1)

L {sin (3 t)} : \frac{3}{s ^{2} + 9}

= \frac{3}{( s + 1 ) ^{2} + 9}

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