laplacetransform t^2cos(8t)

解

ラプラス変換

t^{2} cos (8 t)

- \frac{2 s ( - s ^{2} + 192 )}{( s ^{2} + 64 ) ^{3}}

解答ステップ

L {t^{2} cos (8 t)}

ラプラス変換表を使用する:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

t^{2} cos (8 t)

向け

: f (t) = cos (8 t), k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {cos (8 t)})

L {cos (8 t)} : \frac{s}{s ^{2} + 64}

\frac{d ^{2}}{d s ^{2}} (\frac{s}{s ^{2} + 64}) = - \frac{2 s ( - s ^{2} + 192 )}{( s ^{2} + 64 ) ^{3}}

= (- 1)^{2} (- \frac{2 s ( - s ^{2} + 192 )}{( s ^{2} + 64 ) ^{3}})

= - \frac{2 s ( - s ^{2} + 192 )}{( s ^{2} + 64 ) ^{3}}