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Beliebt Rechnen >

inverselaplace ((s+1)^3)/(s^4)

Lösung

inverse laplace transformation

\frac{( s + 1 ) ^{3}}{s ^{4}}

Lösung

H (t) + 3 t + \frac{3 t ^{2}}{2} + \frac{t ^{3}}{6}

Schritte zur Lösung

L^{- 1} {\frac{( s + 1 ) ^{3}}{s ^{4}}}

Schreibe

\frac{( s + 1 ) ^{3}}{s ^{4}}

um:

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

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

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

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

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

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

L^{- 1} {\frac{1}{s ^{4}}} : \frac{t ^{3}}{6}

= H (t) + 3 t + \frac{3 t ^{2}}{2} + \frac{t ^{3}}{6}

Beliebte Beispiele

derivative 1/(x^6)

d er i v a t i v e \frac{1}{x ^{6}}

derivative of cos^2(2x-x^2)

\frac{d}{d x} (cos^{2} (2 x) - x^{2})

(\partial)/(\partial x)(cos(3x+4y))

\frac{\partial}{\partial x} (cos (3 x + 4 y))

fläche y=x,y=-x+3,y=0

a re a y = x, y = - x + 3, y = 0

integral of (sin^2(2x))

\int (sin^{2} (2 x)) d x