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Beliebt Rechnen >

inverselaplace (9s)/(9s^2+1)

Lösung

inverse laplace transformation

\frac{9 s}{9 s ^{2} + 1}

Lösung

cos (\frac{t}{3})

Schritte zur Lösung

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

= \frac{d}{d t} (L^{- 1} {\frac{9}{9 s ^{2} + 1}}) + L^{- 1} {\frac{9}{9 s ^{2} + 1}} (0)

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

\frac{d}{d t} (3 sin (\frac{t}{3})) = cos (\frac{t}{3})

Evaluiere

3 sin (\frac{t}{3})

am Punkt

0 = 0

= cos (\frac{t}{3})

Beliebte Beispiele

integral of ((x+6))/((x+2)^2)

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

sum from n=1 to infinity of (n^7)/(7^n)

n = 1 \sum \infty \frac{n ^{7}}{7 ^{n}}

y^'+5y=8,y(0)=0

y^{^{'}} + 5 y = 8, y (0) = 0

derivative of xsqrt(100-x^2)

\frac{d}{d x} (x 100 - x^{2})

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

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