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Beliebt Rechnen >

inverselaplace ((s-2)^2)/(s^3)

Lösung

inverse laplace transformation

\frac{( s - 2 ) ^{2}}{s ^{3}}

Lösung

H (t) - 4 t + 2 t^{2}

Schritte zur Lösung

L^{- 1} {\frac{( s - 2 ) ^{2}}{s ^{3}}}

Schreibe

\frac{( s - 2 ) ^{2}}{s ^{3}}

um:

\frac{1}{s} - \frac{4}{s ^{2}} + \frac{4}{s ^{3}}

= L^{- 1} {\frac{1}{s} - \frac{4}{s ^{2}} + \frac{4}{s ^{3}}}

Wende die lineare Eigenschaftder inversen Laplace-Transformation an:

Für Funktionen

f (s), g (s)

und Konstanten

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {\frac{1}{s}} - L^{- 1} {\frac{4}{s ^{2}}} + L^{- 1} {\frac{4}{s ^{3}}}

L^{- 1} {\frac{1}{s}} : H (t)

L^{- 1} {\frac{4}{s ^{2}}} : 4 t

L^{- 1} {\frac{4}{s ^{3}}} : 2 t^{2}

= H (t) - 4 t + 2 t^{2}

Beliebte Beispiele

derivative of 2x^{1/2}+x^{-1}-2

\frac{d}{d x} (2 x^{\frac{1}{2}} + x^{- 1} - 2)

integral of (4sin(x)+(2x^5-sqrt(x))/x)

\int (4 sin (x) + \frac{2 x ^{5} - x}{x}) d x

derivative f(x)=(4x^{3/2})/x

d er i v a t i v e f (x) = \frac{4 x ^{\frac{3}{2}}}{x}

derivative of cos(5x-9)

\frac{d}{d x} (cos (5 x - 9))

inverselaplace (2s)/(s^2+s)

in v erse l a pl a ce \frac{2 s}{s ^{2} + s}