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人気のある微分積分 >

laplacetransform e^{4t}cos(2t)

解

ラプラス変換

e^{4 t} cos (2 t)

解

\frac{s - 4}{( s - 4 ) ^{2} + 4}

解答ステップ

L {e^{4 t} cos (2 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^{4 t} cos (2 t)

向け

: f (t) = cos (2 t), a = 4

= L {cos (2 t)} (s - 4)

L {cos (2 t)} : \frac{s}{s ^{2} + 4}

= \frac{( s - 4 )}{( s - 4 ) ^{2} + 4}

= \frac{s - 4}{( s - 4 ) ^{2} + 4}

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