help with inverse laplace transform (s^2)/((s+2)^4)?!?!?!?

(s^2)/((s+2)^4)

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  • kb
    Lv 7
    7 years ago
    Favorite Answer

    s^2/(s+2)^4

    = [(s+2) - 2]^2 / (s+2)^4

    = ((s+2)^2 - 4(s+2) + 4) / (s+2)^4

    = 1/(s+2)^2 - 4/(s+2)^3 + 4/(s+2)^4. (Alternately, use partial fractions to obtain this.)

    Inverting term by term:

    te^(-2t) - 4(t^2/2!)e^(-2t) + 4(t^3/3!)e^(-2t)

    = e^(-2t) (t - 2t^2 + (2/3)t^3).

    I hope this helps!

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