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Beliebt Rechnen >

laplacetransform (t-1)cos(4(t-1))

Lösung

laplace transformation

(t - 1) cos (4 (t - 1))

Lösung

- \frac{- cos ( 4 ) s ^{2} - 8 sin ( 4 ) s + 16 cos ( 4 )}{( s ^{2} + 16 ) ^{2}} - \frac{cos ( 4 ) s + 4 sin ( 4 )}{s ^{2} + 16}

Schritte zur Lösung

L {cos (4 (t - 1)) (t - 1)}

Schreibe

(t - 1) cos (4 (t - 1))

um:

t cos (4 t - 4) - cos (4 t - 4)

= L {t cos (4 t - 4) - cos (4 t - 4)}

Verwende die lineare Eigenschaft der Laplace-Transformation:

Für Funktionen

f (t), g (t)

und Konstanten

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t cos (4 t - 4)} - L {cos (4 t - 4)}

L {t cos (4 t - 4)} : - \frac{- cos ( 4 ) s ^{2} - 8 sin ( 4 ) s + 16 cos ( 4 )}{( s ^{2} + 16 ) ^{2}}

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

= - \frac{- cos ( 4 ) s ^{2} - 8 sin ( 4 ) s + 16 cos ( 4 )}{( s ^{2} + 16 ) ^{2}} - \frac{cos ( 4 ) s + 4 sin ( 4 )}{s ^{2} + 16}

Beliebte Beispiele

(x-1)y^'+xy=6e^x

(x - 1) y^{^{'}} + x y = 6 e^{x}

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\int tan^{3} (x) (sec (x))^{- \frac{1}{2}} d x

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