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Beliebt Rechnen >

inverselaplace (400)/(25s(s^2+200))

Lösung

inverse laplace transformation

\frac{400}{25 s ( s ^{2} + 200 )}

Lösung

\frac{2}{25} H (t) - \frac{2}{25} cos (102 t)

Schritte zur Lösung

L^{- 1} {\frac{400}{25 s ( s ^{2} + 200 )}}

Ermittle den Partialbruch von

\frac{400}{25 s ( s ^{2} + 200 )} : \frac{2}{25 s} - \frac{2 s}{25 ( s ^{2} + 200 )}

= L^{- 1} {\frac{2}{25 s} - \frac{2 s}{25 ( s ^{2} + 200 )}}

Wende die lineare Eigenschaftder inversen Laplace-Transformation an:

Für Funktionen

f (s), g (s)

und Konstanten

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {\frac{2}{25 s}} - L^{- 1} {\frac{2 s}{25 ( s ^{2} + 200 )}}

L^{- 1} {\frac{2}{25 s}} : \frac{2}{25} H (t)

L^{- 1} {\frac{2 s}{25 ( s ^{2} + 200 )}} : \frac{2}{25} cos (102 t)

= \frac{2}{25} H (t) - \frac{2}{25} cos (102 t)

Beliebte Beispiele

tangent y=tan(x),(pi/4 ,1)

t an g e n t y = tan (x), (\frac{π}{4}, 1)

integral from 8 to 12 of 2/(x^3)

\int_{8}^{12} \frac{2}{x ^{3}} d x

integral of (xln(x))^2

\int (x ln (x))^{2} d x

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x \to 0 lim (x sin (\frac{7 π}{x}))

normal 2x^2-3x+6,\at x=2

n or ma l 2 x^{2} - 3 x + 6, at x = 2