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Beliebt Rechnen >

inverselaplace (s+3)/((s+3)^2+25)

Lösung

inverse laplace transformation

\frac{s + 3}{( s + 3 ) ^{2} + 25}

Lösung

e^{- 3 t} cos (5 t)

Schritte zur Lösung

L^{- 1} {\frac{s + 3}{( s + 3 ) ^{2} + 25}}

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} + 25} : a = - 3, F (s) = \frac{s}{s ^{2} + 25}

= e^{- 3 t} L^{- 1} {\frac{s}{s ^{2} + 25}}

L^{- 1} {\frac{s}{s ^{2} + 25}} : cos (5 t)

= e^{- 3 t} cos (5 t)

Beliebte Beispiele

integral of sec^3(6x)

\int sec^{3} (6 x) d x

fläche-x,x,-2x+6

a re a - x, x, - 2 x + 6

integral of (x-x^2)/(2\sqrt[3]{x)}

\int \frac{x - x ^{2}}{2 3 x} d x

(\partial)/(\partial x)(-5e^xln(y))

\frac{\partial}{\partial x} (- 5 e^{x} ln (y))

fläche y=x^2,y=3x+4

a re a y = x^{2}, y = 3 x + 4