laplacetransform t^2cos(8t)

Lösung

laplace transformation

t^{2} cos (8 t)

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

Schritte zur Lösung

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

Wende Laplace-Transformationstabelle an:

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

Für

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

\frac{d}{d x} (x^{3} - 8 x^{2} + 31 x)

\frac{d ^{2}}{d x ^{2}} (x^{2} e^{x})

n = 0 \sum \infty - 3^{n}

t an g e n t \frac{7}{x}

\int \frac{1}{- x ^{2} + 4 x - 1} d x