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Beliebt Rechnen >

inverselaplace 1/(s^2+4s+12)

Lösung

inverse laplace transformation

\frac{1}{s ^{2} + 4 s + 12}

Lösung

e^{- 2 t} \frac{1}{2 2} sin (22 t)

Schritte zur Lösung

L^{- 1} {\frac{1}{s ^{2} + 4 s + 12}}

\frac{1}{s ^{2} + 4 s + 12} = \frac{1}{( s + 2 ) ^{2} + 8}

= L^{- 1} {\frac{1}{( s + 2 ) ^{2} + 8}}

Wende inverse Transformationsregel an: if

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

dann

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

Für

\frac{1}{( s + 2 ) ^{2} + 8} : a = - 2, F (s) = \frac{1}{s ^{2} + 8}

= e^{- 2 t} L^{- 1} {\frac{1}{s ^{2} + 8}}

L^{- 1} {\frac{1}{s ^{2} + 8}} : \frac{1}{2 2} sin (22 t)

= e^{- 2 t} \frac{1}{2 2} sin (22 t)

Beliebte Beispiele

derivative of (7x+3^2)

\frac{d}{d x} ((7 x + 3)^{2})

derivative of (3x^3+1(-4x^2-3)^4)

\frac{d}{d x} ((3 x^{3} + 1) (- 4 x^{2} - 3)^{4})

limit as x approaches 4 of (x^2-6)/(x-4)

x \to 4 lim (\frac{x ^{2} - 6}{x - 4})

integral of (sqrt(t))/(1+t)

\int \frac{t}{1 + t} d t

derivative 14*((-x+2)/(x^2))

d er i v a t i v e 14 \cdot (\frac{- x + 2}{x ^{2}})