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Beliebt Rechnen >

laplacetransform t^2sin(4t)

Lösung

laplace transformation

t^{2} sin (4 t)

Lösung

- \frac{8 ( - 3 s ^{2} + 16 )}{( s ^{2} + 16 ) ^{3}}

Schritte zur Lösung

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

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

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

\frac{d ^{2}}{d s ^{2}} (\frac{4}{s ^{2} + 16}) = - \frac{8 ( - 3 s ^{2} + 16 )}{( s ^{2} + 16 ) ^{3}}

= (- 1)^{2} (- \frac{8 ( - 3 s ^{2} + 16 )}{( s ^{2} + 16 ) ^{3}})

= - \frac{8 ( - 3 s ^{2} + 16 )}{( s ^{2} + 16 ) ^{3}}

Beliebte Beispiele

inverselaplace F(s)=(s+9)/(s^2-2s-3)

in v erse l a pl a ce F (s) = \frac{s + 9}{s ^{2} - 2 s - 3}

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d er i v a t i v e 3 x (18 x^{4} + \frac{13}{x + 1})

(12y^2-xy)dx+x^2dy=0

(12 y^{2} - x y) d x + x^{2} d y = 0

integral of 4/(5-3x)

\int \frac{4}{5 - 3 x} d x