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Beliebt Rechnen >

laplacetransform t*cos(kt)

Lösung

laplace transformation

t \cdot cos (k t)

Lösung

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

Schritte zur Lösung

L {t cos (k t)}

Wende Laplace-Transformationstabelle an:

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

Für

t cos (k t) : f (t) = cos (k t), k = 1

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

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

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

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

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

Beliebte Beispiele

integral of 1/(9x-4)

integral of (x^2-2x)/(x^3-3x^2+1)

derivative of e^{sin(x}*cos(sin(x)))

y^'-8/x y=(y^4)/(x^{18)}

integral of X^2