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Beliebt Rechnen >

inverselaplace (-s)/(7s^2+26s+25)

Lösung

inverse laplace transformation

\frac{- s}{7 s ^{2} + 26 s + 25}

Lösung

- \frac{1}{7} e^{- \frac{13 t}{7}} cos (\frac{6 t}{7}) + \frac{13 e ^{- \frac{13 t}{7}} sin ( \frac{6 t}{7} )}{7 6}

Schritte zur Lösung

L^{- 1} {\frac{- s}{7 s ^{2} + 26 s + 25}}

Schreibe

\frac{- s}{7 s ^{2} + 26 s + 25}

um:

- \frac{1}{7} \cdot \frac{s + \frac{13}{7}}{( s + \frac{13}{7} ) ^{2} + \frac{6}{49}} + \frac{13}{49} \cdot \frac{1}{( s + \frac{13}{7} ) ^{2} + \frac{6}{49}}

= L^{- 1} {- \frac{1}{7} \cdot \frac{s + \frac{13}{7}}{( s + \frac{13}{7} ) ^{2} + \frac{6}{49}} + \frac{13}{49} \cdot \frac{1}{( s + \frac{13}{7} ) ^{2} + \frac{6}{49}}}

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)}

= - \frac{1}{7} L^{- 1} {\frac{s + \frac{13}{7}}{( s + \frac{13}{7} ) ^{2} + \frac{6}{49}}} + \frac{13}{49} L^{- 1} {\frac{1}{( s + \frac{13}{7} ) ^{2} + \frac{6}{49}}}

L^{- 1} {\frac{s + \frac{13}{7}}{( s + \frac{13}{7} ) ^{2} + \frac{6}{49}}} : e^{- \frac{13 t}{7}} cos (\frac{6 t}{7})

L^{- 1} {\frac{1}{( s + \frac{13}{7} ) ^{2} + \frac{6}{49}}} : e^{- \frac{13 t}{7}} \frac{7}{6} sin (\frac{6 t}{7})

= - \frac{1}{7} e^{- \frac{13 t}{7}} cos (\frac{6 t}{7}) + \frac{13}{49} e^{- \frac{13 t}{7}} \frac{7}{6} sin (\frac{6 t}{7})

Fasse

- \frac{1}{7} e^{- \frac{13 t}{7}} cos (\frac{6 t}{7}) + \frac{13}{49} e^{- \frac{13 t}{7}} \frac{7}{6} sin (\frac{6 t}{7})

zusammen:

- \frac{1}{7} e^{- \frac{13 t}{7}} cos (\frac{6 t}{7}) + \frac{13 e ^{- \frac{13 t}{7}} sin ( \frac{6 t}{7} )}{7 6}

= - \frac{1}{7} e^{- \frac{13 t}{7}} cos (\frac{6 t}{7}) + \frac{13 e ^{- \frac{13 t}{7}} sin ( \frac{6 t}{7} )}{7 6}

Beliebte Beispiele

derivative of sqrt(7x+3)

\frac{d}{d x} (7 x + 3)

limit as n approaches infinity of (3n^{0.4+1}+7n)/(3n^{0.4)+7n}

n \to \infty lim (\frac{3 n ^{0.4 + 1} + 7 n}{3 n ^{0.4} + 7 n})

y^{''}+5y^'=e^{-t},y(0)=-0,y^'(0)=1

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = - 0, y^{^{'}} (0) = 1

integral of (-y)/(cot(x))

\int \frac{- y}{cot ( x )} d x

y^{''}+2y^'-24y=0

y^{^{''}} + 2 y^{^{'}} - 24 y = 0