laplacetransform tcos(4t)

Lösung

laplace transformation

t cos (4 t)

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

Schritte zur Lösung

L {t 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 cos (4 t) : f (t) = cos (4 t), k = 1

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

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

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

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

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

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