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Beliebt Rechnen >

inverselaplace 8/(s^2+9)*e^{-5s}

Lösung

inverse laplace transformation

\frac{8}{s ^{2} + 9} \cdot e^{- 5 s}

Lösung

H (t - 5) \frac{8}{3} sin (3 (t - 5))

Schritte zur Lösung

L^{- 1} {e^{- 5 s} \frac{8}{s ^{2} + 9}}

Wende inverse Transformationsregel an: if

L^{- 1} {F (s)} = f (t)

dann

L^{- 1} {e^{- a s} F (s)} = H (t - a) f (t - a)

Wo

H (t)

Heaviside (Schritt) Funktion ist

= H (t - 5) L^{- 1} {\frac{8}{s ^{2} + 9}} (t - 5)

L^{- 1} {\frac{8}{s ^{2} + 9}} : \frac{8}{3} sin (3 t)

= H (t - 5) \frac{8}{3} sin (3 (t - 5))

Beliebte Beispiele

integral of 3sin(x/2)-2cos((2x)/5)

\int 3 sin (\frac{x}{2}) - 2 cos (\frac{2 x}{5}) d x

derivative of 2xy^2+4

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

derivative of (1+3x^5)

\frac{d}{d x} ((1 + 3 x)^{5})

integral of 1/(X^2)

\int \frac{1}{X ^{2}} d X

integral of (5x^2-12)/((x^2-6x+13)^2)

\int \frac{5 x ^{2} - 12}{( x ^{2} - 6 x + 13 ) ^{2}} d x