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Second order system rise time question

  1. May 5, 2013 #1
    1. The problem statement, all variables and given/known data

    The question is such :
    System is modeled as : y''+2y'+4y=u(t)
    find the time at which the system goes up 75,90,95 % of its final value.

    2. Relevant equations

    3. The attempt at a solution

    I have no idea how to touch that,I tried to find the source of the regular rise time (from 10 to 90%),and didn't got it.How the hell do I even start?It looks impossible to isolate expression for time,from PE solution . Also,from the answers in the book,the answers are approximations (t for 75% for example is ~0.9sec).

    Thanks in advance.
  2. jcsd
  3. May 5, 2013 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Solve the ODE for y(t) conventionally or use Laplace transforms.

    EDIT: looks like an ugly transcendental equation to get t(y) though. Get out the old Excel spreadsheet!
    Last edited: May 5, 2013
  4. May 7, 2013 #3
    Yea,that is the problem,I wanted to know how to do it without any help of mathlab and such,but it looks like overly nasty equation to solve manually (it has exponent of time coupled with sin and cosine terms)
  5. May 10, 2013 #4


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    Staff: Mentor

    Maybe they just want you to read it off a normalized graph?
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