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System dynamics step/ramp formula

  1. Sep 8, 2006 #1
    HI all, I'm taking a basic system dynamics course and I'm either having a problem with a concept or just with the notation.

    I think the easiest way explain the problem I'm having is with an example ( see jpeg).

    If I have f(t) = 0 when t <= a and [(bt)/(a+b)] - b when t>a I would have the laplace transform that equals int[((bt)/(a+b) - b)* e^(-st) dt] I'm fine with integrating this by hand and coming up with the correct answer, but I'm not sure how to get the answer from the tables. The book I'm using ("system dynamics) by katsuhiko ogata) seems to be a very good book, but there is some notation in there regarding step and ramp functions that I'm not understanding.

    mainly stuff like f(t-a)1(t-a). Can someone explain this notation to me and or how to use the laplace tables when dealing with this kind of function?

    Attached Files:

  2. jcsd
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