inverselaplace (0.07s)/(7s^2+19980)

解

逆ラプラス

\frac{0.07 s}{7 s ^{2} + 19980}

0.01 cos (53.42551 \dots t)

解答ステップ

L^{- 1} {\frac{0.07 s}{7 s ^{2} + 19980}}

逆変換ルールを適用:

L^{- 1} {F (s)} = f (t)

ならば

L^{- 1} {s F (s)} = \frac{d}{d t} f (t) + f (0)

\frac{0.07 s}{7 s ^{2} + 19980}

向け

: F (s) = \frac{0.07}{7 s ^{2} + 19980}

= \frac{d}{d t} (L^{- 1} {\frac{0.07}{7 s ^{2} + 19980}}) + L^{- 1} {\frac{0.07}{7 s ^{2} + 19980}} (0)

L^{- 1} {\frac{0.07}{7 s ^{2} + 19980}} : \frac{0.07}{6 3885} sin (\frac{6 555 t}{7})

\frac{d}{d t} (\frac{0.07}{6 3885} sin (\frac{6 555 t}{7})) = 0.01 cos (53.42551 \dots t)

\frac{0.07}{6 3885} sin (\frac{6 555 t}{7})

を

0 = 0

で評価する

= 0.01 cos (53.42551 \dots t)