inverselaplace s/(s^2+\frac{1){lc}}

解

逆ラプラス

\frac{s}{s ^{2} + \frac{1}{l c}}

l c cos (\frac{1}{l c} t) \frac{1}{l c}

解答ステップ

L^{- 1} {\frac{s}{s ^{2} + \frac{1}{l c}}}

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{s}{s ^{2} + \frac{1}{l c}}

向け

: F (s) = \frac{1}{s ^{2} + \frac{1}{l c}}

= \frac{d}{d t} (L^{- 1} {\frac{1}{s ^{2} + \frac{1}{l c}}}) + L^{- 1} {\frac{1}{s ^{2} + \frac{1}{l c}}} (0)

L^{- 1} {\frac{1}{s ^{2} + \frac{1}{l c}}} : l c sin (\frac{1}{l c} t)

\frac{d}{d t} (l c sin (\frac{1}{l c} t)) = l c cos (\frac{1}{l c} t) \frac{1}{l c}

l c sin (\frac{1}{l c} t)

を

0 = 0

で評価する

= l c cos (\frac{1}{l c} t) \frac{1}{l c}