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Beliebt Rechnen >

inverselaplace 1/((z^2+1)^2)

Lösung

inverse laplace transformation

\frac{1}{( z ^{2} + 1 ) ^{2}}

Lösung

\frac{1}{2} (sin (t) - t cos (t))

Schritte zur Lösung

L^{- 1} {\frac{1}{( z ^{2} + 1 ) ^{2}}}

= L^{- 1} {\frac{1}{2} \cdot \frac{2 \cdot 1 ^{3}}{( z ^{2} + 1 ^{2} ) ^{2}}}

Wende die konstante Multiplikationseigenschaft der inversen Laplace-Transformation an:

Für Funktionen

f (t)

und Konstante

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= \frac{1}{2} L^{- 1} {\frac{2 \cdot 1 ^{3}}{( z ^{2} + 1 ^{2} ) ^{2}}}

Verwende inverse Laplace-Transformationstabelle:

L^{- 1} {\frac{2 a ^{3}}{( s ^{2} + a ^{2} ) ^{2}}} = sin (a t) - a t cos (a t)

L^{- 1} {\frac{2 \cdot 1 ^{3}}{( z ^{2} + 1 ^{2} ) ^{2}}} = sin (t) - t cos (t)

= \frac{1}{2} (sin (t) - t cos (t))

Beliebte Beispiele

(dy)/(dx)=(2y^4+x^4)/(xy^3)

\frac{d y}{d x} = \frac{2 y ^{4} + x ^{4}}{x y ^{3}}

derivative of (4x^2/((7-5x)^3))

\frac{d}{d x} (\frac{4 x ^{2}}{( 7 - 5 x ) ^{3}})

(\partial)/(\partial x)(2y-3/(y^2)+x)

\frac{\partial}{\partial x} (2 y - \frac{3}{y ^{2}} + x)

derivative (x^6-5)sqrt(x)

d er i v a t i v e (x^{6} - 5) x

derivative of (cos(x)/(x+1))

\frac{d}{d x} (\frac{cos ( x )}{x + 1})