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Beliebt Rechnen >

inverselaplace {(4s)/(4s^2+1)}

Lösung

inverse laplace transformation

{\frac{4 s}{4 s ^{2} + 1}}

Lösung

cos (\frac{t}{2})

Schritte zur Lösung

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

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{4 s}{4 s ^{2} + 1} : F (s) = \frac{4}{4 s ^{2} + 1}

= \frac{d}{d t} (L^{- 1} {\frac{4}{4 s ^{2} + 1}}) + L^{- 1} {\frac{4}{4 s ^{2} + 1}} (0)

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

\frac{d}{d t} (2 sin (\frac{t}{2})) = cos (\frac{t}{2})

Evaluiere

2 sin (\frac{t}{2})

am Punkt

0 = 0

= cos (\frac{t}{2})

Beliebte Beispiele

limit as x approaches 0 of 2x-x^2-x^3

x \to 0 lim (2 x - x^{2} - x^{3})

integral of cos(x^5)

\int cos (x^{5}) d x

inverselaplace 3/(s^2-25)

in v erse l a pl a ce \frac{3}{s ^{2} - 25}

derivative sin(x)+7/4 cot(x)

d er i v a t i v e sin (x) + \frac{7}{4} cot (x)

steigung (x^2)/(x+7)

s l o p e \frac{x ^{2}}{x + 7}