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Beliebt Rechnen >

inverselaplace 1/(s^2+2pis+pi^2)

Lösung

inverse laplace transformation

\frac{1}{s ^{2} + 2 \cdot π \cdot s + π ^{2}}

Lösung

e^{- π t} t

Schritte zur Lösung

L^{- 1} {\frac{1}{s ^{2} + 2 π s + π ^{2}}}

\frac{1}{s ^{2} + 2 π s + π ^{2}} = \frac{1}{( s + π ) ^{2}}

= L^{- 1} {\frac{1}{( s + π ) ^{2}}}

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

= e^{- π t} L^{- 1} {\frac{1}{s ^{2}}}

L^{- 1} {\frac{1}{s ^{2}}} : t

= e^{- π t} t

Beliebte Beispiele

sum from n=3 to infinity of e^{5-6n}

n = 3 \sum \infty e^{5 - 6 n}

(d^2y)/(dx^2)-(dy)/(dx)-2y=0

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 0

derivative tan(x)-1sec(x)

d er i v a t i v e tan (x) - 1 sec (x)

integral of sqrt(y^2+1)

\int y^{2} + 1 d y

tangent y=sin(sin(x)),\at x=pi

t an g e n t y = sin (sin (x)), at x = π