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Beliebt Rechnen >

inverselaplace (s+3)/((s+3)^2+4)

Lösung

inverse laplace transformation

\frac{s + 3}{( s + 3 ) ^{2} + 4}

Lösung

e^{- 3 t} cos (2 t)

Schritte zur Lösung

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

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 + 3}{( s + 3 ) ^{2} + 4} : a = - 3, F (s) = \frac{s}{s ^{2} + 4}

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

L^{- 1} {\frac{s}{s ^{2} + 4}} : cos (2 t)

= e^{- 3 t} cos (2 t)

Beliebte Beispiele

derivative of 1/2 cos(x/2)

\frac{d}{d x} (\frac{1}{2} cos (\frac{x}{2}))

y^{^{'}} = y^{2} + y

derivative of (3x+2^6)

\frac{d}{d x} ((3 x + 2)^{6})

integral from-7 to 7 of 1/x

\int_{- 7}^{7} \frac{1}{x} d x

tangent y= x/(sqrt(9+x^2)),(0,0)

t an g e n t y = \frac{x}{9 + x ^{2}}, (0, 0)