Laplace Transforms: ( 100(s+10) ) / ( s(s+5)(s+20) ) and....

tragicallylost

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Apr 17, 2007
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hello. im having trouble with a problem i hope i can get some hlep with. Here is the problem:

Find the invers (unilateral) Laplace Transforms of the following functions:

1) (100(s+10))/(s(s+5)(s+20))

2) (4/(s(s+2)squared(s+4))

I try to approch it by litting the denomiantor = zero, and solve for s. But it's not working. So, please i need help with this problem.
 
Re: Laplace Transforms

hello. im having trouble with a problem i hope i can get some hlep with. Here is the problem:

Find the invers (unilateral) Laplace Transforms of the following functions:

\(\displaystyle \L\\\frac{100(s+10)}{s(s+5)(s+20)}\)

Break it up into its partial fraction and find each portion.

\(\displaystyle \L\\\frac{-10}{3(s+20)}-\frac{20}{3(s+5)}+\frac{10}{s}\)

\(\displaystyle \L\\L^{-1}=\frac{-20}{3}e^{-5t}-\frac{10}{3}e^{-20t}+10\)



\(\displaystyle \L\\\frac{4}{s(s+2)^{2}(s+4)}\)

\(\displaystyle \L\\=\frac{-1}{4(s+4)}-\frac{1}{(s+2)^{2}}+\frac{1}{4s}\)

\(\displaystyle \L\\L^{-1}=-te^{-2t}-\frac{1}{4}e^{-4t}+\frac{1}{4}\)
 
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