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Beliebt Rechnen >

laplacetransform e^{-4t}*cos(3t)

Lösung

laplace transformation

e^{- 4 t} \cdot cos (3 t)

Lösung

\frac{s + 4}{( s + 4 ) ^{2} + 9}

Schritte zur Lösung

L {e^{- 4 t} cos (3 t)}

Wende Transformationsregel an: wenn

L {f (t)} = F (s)

dann

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

Für

e^{- 4 t} cos (3 t) : f (t) = cos (3 t), a = - 4

= L {cos (3 t)} (s + 4)

L {cos (3 t)} : \frac{s}{s ^{2} + 9}

= \frac{( s + 4 )}{( s + 4 ) ^{2} + 9}

= \frac{s + 4}{( s + 4 ) ^{2} + 9}

Beliebte Beispiele

integral of cos^2(8x)

\int cos^{2} (8 x) d x

integral of θ^2

\int θ^{2} d θ

sum from n=1 to infinity of (-1)^nn^2

n = 1 \sum \infty (- 1)^{n} n^{2}

integral of (5x^2-9)/(x^3-9x)

\int \frac{5 x ^{2} - 9}{x ^{3} - 9 x} d x

derivative f(x)=(x-5)/(x+5)

d er i v a t i v e f (x) = \frac{x - 5}{x + 5}