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Beliebt Rechnen >

inverselaplace (-5e^{(-s)})/((s^2+6s+25))

Lösung

inverse laplace transformation

\frac{- 5 e ^{(- s)}}{( s ^{2} + 6 s + 25 )}

Lösung

- \frac{5}{4} e^{- 3 (t - 1)} H (t - 1) sin (4 (t - 1))

Schritte zur Lösung

L^{- 1} {\frac{- 5 e ^{(- s)}}{( s ^{2} + 6 s + 25 )}}

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 - 1) L^{- 1} {\frac{- 5}{s ^{2} + 6 s + 25}} (t - 1)

L^{- 1} {\frac{- 5}{s ^{2} + 6 s + 25}} : - \frac{5}{4} e^{- 3 t} sin (4 t)

= H (t - 1) (- \frac{5}{4} e^{- 3 (t - 1)} sin (4 (t - 1)))

= - \frac{5}{4} e^{- 3 (t - 1)} H (t - 1) sin (4 (t - 1))

Beliebte Beispiele

f(x)=ln(sech(2x))

f (x) = ln (sech (2 x))

integral of x^2sin(3x)

\int x^{2} sin (3 x) d x

(dy)/(dx)=tan^2(x)

\frac{d y}{d x} = tan^{2} (x)

(d^2)/(dx^2)((3x+4)/(2x-5))

\frac{d ^{2}}{d x ^{2}} (\frac{3 x + 4}{2 x - 5})

integral of 1/((cos(x))^2)

\int \frac{1}{( cos ( x ) ) ^{2}} d x