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Beliebt Rechnen >

inverselaplace (s+2)/(s^2+4s+6)

Lösung

inverse laplace transformation

\frac{s + 2}{s ^{2} + 4 s + 6}

Lösung

e^{- 2 t} cos (2 t)

Schritte zur Lösung

L^{- 1} {\frac{s + 2}{s ^{2} + 4 s + 6}}

\frac{s + 2}{s ^{2} + 4 s + 6} = \frac{s + 2}{( s + 2 ) ^{2} + 2}

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

Wende inverse Transformationsregel an: if

L^{- 1} {F (s)} = f (t)

dann

L^{- 1} {F (s - a)} = e^{a t} f (t)

Für

\frac{s + 2}{( s + 2 ) ^{2} + 2} : a = - 2, F (s) = \frac{s}{s ^{2} + 2}

= e^{- 2 t} L^{- 1} {\frac{s}{s ^{2} + 2}}

L^{- 1} {\frac{s}{s ^{2} + 2}} : cos (2 t)

= e^{- 2 t} cos (2 t)

Beliebte Beispiele

derivative of (2/5 ^{sqrt(x)})

\frac{d}{d x} ((\frac{2}{5})^{x})

integral of (1+x)(2x+x^2)^5

\int (1 + x) (2 x + x^{2})^{5} d x

derivative f(x)=3t^3-18t^2+2

d er i v a t i v e f (x) = 3 t^{3} - 18 t^{2} + 2

limit as x approaches-infinity of-x

x \to - \infty lim (- x)

integral of 8x(4x^2+4)^4

\int 8 x (4 x^{2} + 4)^{4} d x