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Beliebt Rechnen >

inverselaplace 1/(s^2+6s+25)

Lösung

inverse laplace transformation

\frac{1}{s ^{2} + 6 s + 25}

Lösung

e^{- 3 t} \frac{1}{4} sin (4 t)

Schritte zur Lösung

L^{- 1} {\frac{1}{s ^{2} + 6 s + 25}}

\frac{1}{s ^{2} + 6 s + 25} = \frac{1}{( s + 3 ) ^{2} + 16}

= L^{- 1} {\frac{1}{( s + 3 ) ^{2} + 16}}

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 + 3 ) ^{2} + 16} : a = - 3, F (s) = \frac{1}{s ^{2} + 16}

= e^{- 3 t} L^{- 1} {\frac{1}{s ^{2} + 16}}

L^{- 1} {\frac{1}{s ^{2} + 16}} : \frac{1}{4} sin (4 t)

= e^{- 3 t} \frac{1}{4} sin (4 t)

Beliebte Beispiele

integral of (cos(3x)-sin(x))

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

integral from-infinity to 0 of 1/(2-5x)

\int_{- \infty}^{0} \frac{1}{2 - 5 x} d x

derivative y=x^3-2x+1

d er i v a t i v e y = x^{3} - 2 x + 1

integral of 1/((9-x)^{3/2)}

\int \frac{1}{( 9 - x ) ^{\frac{3}{2}}} d x

integral of sin(3/4)xcos^2(3/4)x

\int sin (\frac{3}{4}) x cos^{2} (\frac{3}{4}) x d x