inverselaplace 2/((s+1)^3)

解答

的拉普拉斯逆变换

\frac{2}{( s + 1 ) ^{3}}

e^{- t} t^{2}

求解步骤

L^{- 1} {\frac{2}{( s + 1 ) ^{3}}}

应用逆变换法则: if

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

则

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

对于

\frac{2}{( s + 1 ) ^{3}} : a = - 1, F (s) = \frac{2}{s ^{3}}

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

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

= e^{- t} t^{2}

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