laplacetransform t^2cos(4t)

Lösung

laplace transformation

t^{2} cos (4 t)

- \frac{2 s ( - s ^{2} + 48 )}{( s ^{2} + 16 ) ^{3}}

Schritte zur Lösung

L {t^{2} cos (4 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 (4 t) : f (t) = cos (4 t), k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {cos (4 t)})

L {cos (4 t)} : \frac{s}{s ^{2} + 16}

\frac{d ^{2}}{d s ^{2}} (\frac{s}{s ^{2} + 16}) = - \frac{2 s ( - s ^{2} + 48 )}{( s ^{2} + 16 ) ^{3}}

= (- 1)^{2} (- \frac{2 s ( - s ^{2} + 48 )}{( s ^{2} + 16 ) ^{3}})

= - \frac{2 s ( - s ^{2} + 48 )}{( s ^{2} + 16 ) ^{3}}

\int ye d y

\int cos (x) 9 - sin^{2} (x) d x

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