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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

derivative of 3+cos(x)

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

sum from n=0 to infinity}e^{-n of+1

n = 0 \sum \infty e^{- n} + 1

integral of x/(sqrt(4+x^2))

\int \frac{x}{4 + x ^{2}} d x

derivative (x^5+e^x)/(x+2)

d er i v a t i v e \frac{x ^{5} + e ^{x}}{x + 2}

integral from e to infinity of x^0ln(x)

\int_{e}^{\infty} x^{0} ln (x) d x