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Inverse laplace transform of this simple function?

  1. Jul 4, 2013 #1
    what is the inverse laplace transform of (2s)(1/(s-2))?

    could i use the identity ∫f(T)g(t-T)dT=F(s)G(s)?

    i was hesitant so i figured i'd just ask before i continue..
     
  2. jcsd
  3. Jul 4, 2013 #2

    lurflurf

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    write

    $$\frac{s}{s-2}=\frac{s-2+2}{s-2}=1+\frac{2}{s-2}$$

    or go ahead and use convolution
     
  4. Jul 4, 2013 #3

    Ray Vickson

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    You could use the property
    [tex] \cal{L}(f^\prime)(s) = s\, \cal{L}(f)(s) - f(0+)[/tex]
    Be careful, though: that is for a LT defined as
    [tex] \cal{L}(f)(s) = \int_{0+}^{\infty} e^{-st} f(t) \, dt. [/tex]
    If, instead, you prefer to define your LT as
    [tex] \cal{L}(f)(s) = \int_{0-}^{\infty} e^{-st} f(t) \, dt, [/tex]
    then you will need
    [tex]\cal{L}(f^\prime)(s) = s\, \cal{L}(f)(s) - f(0-)[/tex]
     
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