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Beliebt Rechnen >

inverselaplace s/(s^2-14s+1)

Lösung

inverse laplace transformation

\frac{s}{s ^{2} - 14 s + 1}

Lösung

e^{7 t} cosh (43 t) + \frac{7}{4 3} e^{7 t} sinh (43 t)

Schritte zur Lösung

L^{- 1} {\frac{s}{s ^{2} - 14 s + 1}}

Schreibe

\frac{s}{s ^{2} - 14 s + 1}

um:

\frac{s - 7}{( s - 7 ) ^{2} - 48} + 7 \cdot \frac{1}{( s - 7 ) ^{2} - 48}

= L^{- 1} {\frac{s - 7}{( s - 7 ) ^{2} - 48} + 7 \cdot \frac{1}{( s - 7 ) ^{2} - 48}}

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{s - 7}{( s - 7 ) ^{2} - 48}} + 7 L^{- 1} {\frac{1}{( s - 7 ) ^{2} - 48}}

L^{- 1} {\frac{s - 7}{( s - 7 ) ^{2} - 48}} : e^{7 t} cosh (43 t)

L^{- 1} {\frac{1}{( s - 7 ) ^{2} - 48}} : e^{7 t} \frac{1}{4 3} sinh (43 t)

= e^{7 t} cosh (43 t) + 7 e^{7 t} \frac{1}{4 3} sinh (43 t)

Fasse

e^{7 t} cosh (43 t) + 7 e^{7 t} \frac{1}{4 3} sinh (43 t)

zusammen:

e^{7 t} cosh (43 t) + \frac{7}{4 3} e^{7 t} sinh (43 t)

= e^{7 t} cosh (43 t) + \frac{7}{4 3} e^{7 t} sinh (43 t)

Beliebte Beispiele

laplacetransform t*e^{2t}

l a pl a ce t r an s f or m t \cdot e^{2 t}

(dy)/(dt)+1/2 y= 1/2 e^{t/3}

\frac{d y}{d t} + \frac{1}{2} y = \frac{1}{2} e^{\frac{t}{3}}

sum from n=0 to infinity of 5(-10/11)^n

n = 0 \sum \infty 5 (- \frac{10}{11})^{n}

limit as x approaches 0-of arctan(x)

x \to 0 - lim (arctan (x))

integral of (3x^2+1)^6

\int (3 x^{2} + 1)^{6} d x