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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 (3x^5-7x^3)/(x^2)

\int \frac{3 x ^{5} - 7 x ^{3}}{x ^{2}} d x

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

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

derivative of 6x^2-18x+12

\frac{d}{d x} (6 x^{2} - 18 x + 12)

fläche x^2,-4,0

a re a x^{2}, - 4, 0

integral of x^5sqrt(x^3)+4

\int x^{5} x^{3} + 4 d x