inverselaplace a/(s^2+a^2)

Lösung

inverse laplace transformation

\frac{a}{s ^{2} + a ^{2}}

\frac{a sin ( t a ^{2} )}{a ^{2}}

Schritte zur Lösung

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

= L^{- 1} ⎩ ⎨ ⎧ \frac{a}{a ^{2}} \cdot \frac{a ^{2}}{s ^{2} + ( a ^{2} ) ^{2}} ⎭ ⎬ ⎫

Wende die konstante Multiplikationseigenschaft der inversen Laplace-Transformation an:

Für Funktionen

f (t)

und Konstante

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= \frac{a}{a ^{2}} L^{- 1} ⎩ ⎨ ⎧ \frac{a ^{2}}{s ^{2} + ( a ^{2} ) ^{2}} ⎭ ⎬ ⎫

Verwende inverse Laplace-Transformationstabelle:

L^{- 1} {\frac{a}{s ^{2} + a ^{2}}} = sin (a t)

L^{- 1} {\frac{a ^{2}}{s ^{2} + ( a ^{2} ) ^{2}}} = sin (a^{2} t)

= \frac{a}{a ^{2}} sin (a^{2} t)

= \frac{a sin ( t a ^{2} )}{a ^{2}}

\frac{x ^{2}}{y ^{2} - 2} \frac{d y}{d x} = \frac{1}{2 y}

\int_{- 10}^{10} (x^{2} + x) d x

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

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

d er i v a t i v e - \frac{4}{x ^{3}}