What is inverse oflaplace e^{-pis} 2/(s^3) ?

The answer to inverse oflaplace e^{-pis} 2/(s^3) is \H(t-pi)(t-pi)^2

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inverse oflaplace e^{-pis} 2/(s^3)

inverselaplace

H (t - π) (t - π)^{2}

Solution steps

L^{- 1} {e^{- π s} \frac{2}{s ^{3}}}

Apply inverse transform rule:

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

then

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

Where

H (t)

is Heaviside step function

= H (t - π) L^{- 1} {\frac{2}{s ^{3}}} (t - π)

L^{- 1} {\frac{2}{s ^{3}}} : t^{2}

= H (t - π) (t - π)^{2}

What is inverse oflaplace e^{-pis} 2/(s^3) ?
The answer to inverse oflaplace e^{-pis} 2/(s^3) is \H(t-pi)(t-pi)^2