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Laplace and differential equation problem.HELP!

  1. Dec 5, 2008 #1
    1. The problem statement, all variables and given/known data

    I have this parallel system and i have found its transfer function.Now i have to find what is the differential equation that links the input and the output

    2. Relevant equations

    u(t)=input, w(t)=output H(s)=w(s)/u(s)=s+1/s(s+1)+1 -->transfer function

    3. The attempt at a solution

    I think i have to go backwards starting from H(s) but i dont know how to do it

    Any help???
     
  2. jcsd
  3. Dec 5, 2008 #2

    CEL

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    Multiply w by the denominator and u by the numerator of the TF.
    Remember that the inverse transform of sF(s) is [tex]\frac{df}{dt} - f(0^-)[/tex] and that of [tex]s^2F(s)[/tex] is [tex]\frac{d^2f}{dt^2} - \frac{df}{dt}(0^-) - f(0^-)[/tex].
     
  4. Dec 5, 2008 #3
    Thank you.I did it and i found a DE. Don't know yet if it is correct,though.I will tell you as soon as my teacher grades my paper.Thank for the help,though. I really appreciate it.
     
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