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Beliebt Rechnen >

inverselaplace (3s)/((s^2+4))

Lösung

inverse laplace transformation

\frac{3 s}{( s ^{2} + 4 )}

Lösung

3 cos (2 t)

Schritte zur Lösung

L^{- 1} {\frac{3 s}{( s ^{2} + 4 )}}

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{3 s}{s ^{2} + 4} : F (s) = \frac{3}{s ^{2} + 4}

= \frac{d}{d t} (L^{- 1} {\frac{3}{s ^{2} + 4}}) + L^{- 1} {\frac{3}{s ^{2} + 4}} (0)

L^{- 1} {\frac{3}{s ^{2} + 4}} : \frac{3}{2} sin (2 t)

\frac{d}{d t} (\frac{3}{2} sin (2 t)) = 3 cos (2 t)

Evaluiere

\frac{3}{2} sin (2 t)

am Punkt

0 = 0

= 3 cos (2 t)

Beliebte Beispiele

y^{''''}+2y^{''}+y=0

y^{^{''''}} + 2 y^{^{''}} + y = 0

derivative of ((10/(4+x))^{1/2})

\frac{d}{d x} ((\frac{10}{4 + x})^{\frac{1}{2}})

derivative-1/4 x^4+6x^2

d er i v a t i v e - \frac{1}{4} x^{4} + 6 x^{2}

derivative of (x^4/(12))

\frac{d}{d x} (\frac{x ^{4}}{12})

derivative f(x)=4x^2sin(x)+2x

d er i v a t i v e f (x) = 4 x^{2} sin (x) + 2 x