de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

inverselaplace (2s)/((s+3)^2+7)

Lösung

inverse laplace transformation

\frac{2 s}{( s + 3 ) ^{2} + 7}

Lösung

- \frac{6}{7} e^{- 3 t} sin (7 t) + 2 e^{- 3 t} cos (7 t)

Schritte zur Lösung

L^{- 1} {\frac{2 s}{( s + 3 ) ^{2} + 7}}

Schreibe

\frac{2 s}{( s + 3 ) ^{2} + 7}

um:

2 \cdot \frac{s + 3}{( s + 3 ) ^{2} + 7} - 6 \cdot \frac{1}{( s + 3 ) ^{2} + 7}

= L^{- 1} {\frac{2 s}{( s + 3 ) ^{2} + 7}}

Wende inverse Transformationsregel an: if

L^{- 1} {F (s)} = f (t)

dann

L^{- 1} {s F (s)} = \frac{d}{d t} f (t) + f (0)

Für

\frac{2 s}{( s + 3 ) ^{2} + 7} : F (s) = \frac{2}{( s + 3 ) ^{2} + 7}

= \frac{d}{d t} (L^{- 1} {\frac{2}{( s + 3 ) ^{2} + 7}}) + L^{- 1} {\frac{2}{( s + 3 ) ^{2} + 7}} (0)

L^{- 1} {\frac{2}{( s + 3 ) ^{2} + 7}} : e^{- 3 t} \frac{2}{7} sin (7 t)

\frac{d}{d t} (e^{- 3 t} \frac{2}{7} sin (7 t)) = - \frac{6}{7} e^{- 3 t} sin (7 t) + 2 e^{- 3 t} cos (7 t)

Evaluiere

e^{- 3 t} \frac{2}{7} sin (7 t)

am Punkt

0 = 0

= - \frac{6}{7} e^{- 3 t} sin (7 t) + 2 e^{- 3 t} cos (7 t)

Beliebte Beispiele

limit as x approaches-2 of (x+1)*(x+1)

x \to - 2 lim ((x + 1) \cdot (x + 1))

integral of sqrt(7x+1)

\int 7 x + 1 d x

integral of x\sqrt[3]{5-6x^2}

\int x 3 5 - 6 x^{2} d x

(\partial)/(\partial y)(tan(2x+y))

\frac{\partial}{\partial y} (tan (2 x + y))

0 = 2 x + 1 - 2 y y^{^{'}}