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Beliebt Rechnen >

inverselaplace (s+3)/(s^2+6s+13)

Lösung

inverse laplace transformation

\frac{s + 3}{s ^{2} + 6 s + 13}

Lösung

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

Schritte zur Lösung

L^{- 1} {\frac{s + 3}{s ^{2} + 6 s + 13}}

\frac{s + 3}{s ^{2} + 6 s + 13} = \frac{s + 3}{( s + 3 ) ^{2} + 4}

= 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

integral of (3x-sin(x))

\int (3 x - sin (x)) d x

limit as x approaches 7 of (1/x-1/7)/(x-7)

x \to 7 lim (\frac{\frac{1}{x} - \frac{1}{7}}{x - 7})

integral of sin^2((pix)/2)

\int sin^{2} (\frac{π x}{2}) d x

integral of 1-csc(x)cot(x)

\int 1 - csc (x) cot (x) d x

(\partial)/(\partial y)(3xy+e^{-x^2y})

\frac{\partial}{\partial y} (3 x y + e^{- x^{2} y})