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Beliebt Rechnen >

inverselaplace (7s)/(s^2-2s+10)

Lösung

inverse laplace transformation

\frac{7 s}{s ^{2} - 2 s + 10}

Lösung

7 e^{t} cos (3 t) + \frac{7}{3} e^{t} sin (3 t)

Schritte zur Lösung

L^{- 1} {\frac{7 s}{s ^{2} - 2 s + 10}}

Schreibe

\frac{7 s}{s ^{2} - 2 s + 10}

um:

7 \cdot \frac{s - 1}{( s - 1 ) ^{2} + 9} + 7 \cdot \frac{1}{( s - 1 ) ^{2} + 9}

= L^{- 1} {7 \cdot \frac{s - 1}{( s - 1 ) ^{2} + 9} + 7 \cdot \frac{1}{( s - 1 ) ^{2} + 9}}

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)}

= 7 L^{- 1} {\frac{s - 1}{( s - 1 ) ^{2} + 9}} + 7 L^{- 1} {\frac{1}{( s - 1 ) ^{2} + 9}}

L^{- 1} {\frac{s - 1}{( s - 1 ) ^{2} + 9}} : e^{t} cos (3 t)

L^{- 1} {\frac{1}{( s - 1 ) ^{2} + 9}} : e^{t} \frac{1}{3} sin (3 t)

= 7 e^{t} cos (3 t) + 7 e^{t} \frac{1}{3} sin (3 t)

Fasse

7 e^{t} cos (3 t) + 7 e^{t} \frac{1}{3} sin (3 t)

zusammen:

7 e^{t} cos (3 t) + \frac{7}{3} e^{t} sin (3 t)

= 7 e^{t} cos (3 t) + \frac{7}{3} e^{t} sin (3 t)

Beliebte Beispiele

integral of (2x+5)/(x^2-4x+13)

\int \frac{2 x + 5}{x ^{2} - 4 x + 13} d x

integral of 4/(xsqrt(x^2-1))

\int \frac{4}{x x ^{2} - 1} d x

integral of 4y^2

\int 4 y^{2} d y

derivative of (x^2/(x^2-36))

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 36})

integral of 1/(sqrt(x^2-5))

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