laplacetransform (cos(7t))/(e^{5t)}

解

ラプラス変換

\frac{cos ( 7 t )}{e ^{5 t}}

\frac{s + 5}{( s + 5 ) ^{2} + 49}

解答ステップ

L {\frac{cos ( 7 t )}{e ^{5 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)

\frac{cos ( 7 t )}{e ^{5 t}}

向け

: f (t) = cos (7 t), a = - 5

= L {cos (7 t)} (s + 5)

L {cos (7 t)} : \frac{s}{s ^{2} + 49}

= \frac{( s + 5 )}{( s + 5 ) ^{2} + 49}

= \frac{s + 5}{( s + 5 ) ^{2} + 49}