laplacetransform e^{-43t}*e^{72t}cos(77t)

解

ラプラス変換

e^{- 43 t} \cdot e^{72 t} cos (77 t)

\frac{s - 29}{( s - 29 ) ^{2} + 5929}

解答ステップ

L {e^{- 43 t} e^{72 t} cos (77 t)}

拡張

e^{- 43 t} e^{72 t} cos (77 t) : e^{29 t} cos (77 t)

= L {e^{29 t} cos (77 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^{29 t} cos (77 t)

向け

: f (t) = cos (77 t), a = 29

= L {cos (77 t)} (s - 29)

L {cos (77 t)} : \frac{s}{s ^{2} + 5929}

= \frac{( s - 29 )}{( s - 29 ) ^{2} + 5929}

= \frac{s - 29}{( s - 29 ) ^{2} + 5929}