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Beliebt Rechnen >

inverselaplace 4/(s^2(s^2+16))

Lösung

inverse laplace transformation

\frac{4}{s ^{2} ( s ^{2} + 16 )}

Lösung

\frac{t}{4} - \frac{1}{16} sin (4 t)

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

= L^{- 1} {\frac{1}{4 s ^{2}} - \frac{1}{4 ( s ^{2} + 16 )}}

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

L^{- 1} {\frac{1}{4 s ^{2}}} : \frac{t}{4}

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

= \frac{t}{4} - \frac{1}{16} sin (4 t)

Beliebte Beispiele

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

t an g e n t y = tan (x), at x = π

integral of x^4(5-x^2)

\int x^{4} (5 - x^{2}) d x

(\partial)/(\partial y)(-x/((x+y)^2))

\frac{\partial}{\partial y} (- \frac{x}{( x + y ) ^{2}})

derivative of sqrt(x/(2+cx))

\frac{d}{d x} (\frac{x}{2 + c x})

integral of (sqrt(1-x^2))/(x^2)

\int \frac{1 - x ^{2}}{x ^{2}} d x