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Beliebt Rechnen >

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

Lösung

laplace transformation

e^{- t} cos (4 t)

Lösung

\frac{s + 1}{( s + 1 ) ^{2} + 16}

Schritte zur Lösung

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

Wende Transformationsregel an: wenn

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

dann

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

Für

e^{- t} cos (4 t) : f (t) = cos (4 t), a = - 1

= L {cos (4 t)} (s + 1)

L {cos (4 t)} : \frac{s}{s ^{2} + 16}

= \frac{( s + 1 )}{( s + 1 ) ^{2} + 16}

= \frac{s + 1}{( s + 1 ) ^{2} + 16}

Beliebte Beispiele

integral of (3x^2+2x)e^{(x^3+x^2)}

\int (3 x^{2} + 2 x) e^{(x^{3} + x^{2})} d x

inverselaplace 1/((s-2)(s-2))

in v erse l a pl a ce \frac{1}{( s - 2 ) ( s - 2 )}

derivative (x^2+x)e^x

d er i v a t i v e (x^{2} + x) e^{x}

limit as x approaches 1+of 1/(1-x)

x \to 1 + lim (\frac{1}{1 - x})

integral of (e^{2y}-y)/(e^y)

\int \frac{e ^{2 y} - y}{e ^{y}} d y