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Overdamped system

  1. Jan 12, 2016 #1
    1. The problem statement, all variables and given/known data
    When we have a damped system,we have 3 types of responses of the system,what really determines how our system will behave?
    diffyqs1538x.jpg


    2. Relevant equations
    [tex]\alpha = R/2L[/tex]
    [tex]\Omega = 1/LC[/tex]

    3. The attempt at a solution
    Overdamped system solution is [tex] x(t)=A1*exp(\alpha+\sqrt(\alpha^2-\omega^2) + A2* exp-(\alpha+\sqrt(\alpha^2-\omega^2)[/tex],this green exponential decay is when one of the constants is zero I guess,because then we have exp(-t),what about other curves?
     
    Last edited by a moderator: Jan 12, 2016
  2. jcsd
  3. Jan 12, 2016 #2

    donpacino

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    I suggest you look at the system in the frequency domain.
     
  4. Jan 12, 2016 #3

    Mark44

    Staff: Mentor

    Your solution should be a function of t, which doesn't appear on the right side above.
    The system is modelled by a 2nd order differential equation. The roots of the characteristic equation for the differential equation determine whether the system is overdamped, underdamped, or critically damped.
     
  5. Jan 13, 2016 #4
    Yes,I know that roots determine system behaviour,what I wonder is about DAMPED system,we have 3 variations of the response and I forgout to multiply by t
     
  6. Jan 23, 2016 #5
    I am really sad that none actually understood my question,what I figured out,those 3 graphs are determined by initial conditions, for the blue one if the capacitor has initial voltage as on the picture it will produce a current that has the same direction as the initial current of the inductor,that's why we have a little 'spike' over value of 1.(they are being added up)

    The red graph ,is when we have initial voltage on the capacitor producing a current in ic in the opposite direction of the initial current in the inductor ,and therefore we have a negative 'spike' ,because in the scenario of the blue graph currents add up,and here one current will have bigger value than the other one.

    What about the green graph,I am not quite sure about it?
     

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  7. Jan 24, 2016 #6

    NascentOxygen

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    The middle graph is what would result when the capacitor has an initial voltage but there is no initial current in the inductor.

    I think you might have the direction of initial IL around the wrong way for red and blue, but anyway your idea sounds spot on.

    I'm not sure that the values of RC and L that give rise to the red curve would, without change, also be able to produce the blue and green curves, but a simulation would easily confirm this is so just by setting different values for IL(0).
     
  8. Jan 24, 2016 #7
    Do you have a suggestion for some good simulation program?Maybe proteus demo?
     
  9. Jan 24, 2016 #8

    donpacino

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  10. Jan 24, 2016 #9

    donpacino

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    write the equations for the circuit out. In your initial post you gave us no indication of what this system was...........
     
  11. Jan 24, 2016 #10
    I wrote that it's a overdamped system ,and gave you the equation of the system,I really don't see how equations gonna help you out with this one?
     
  12. Jan 24, 2016 #11

    donpacino

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    If you either
    A. disregaurd our advice
    or
    B. don't give us the information we need to give you advice

    don't be upset when you are not happy with the results.

    Looking at the governing equations (preferably in the frequency domain) will tell you how the component values and the initial conditions will effect the transient conditions.

    where did you get the equation from post #1?
    is there any other information you are withholding from us?
     
  13. Jan 24, 2016 #12

    donpacino

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    what is your backround in electronics?

    IL(0-) cannot be anything but 0 (assuming the switch closes at t=0)

    if it opens at t=0 that is a different story
     
  14. Jan 25, 2016 #13
    Check your equation again.
     

    Attached Files:

  15. Jan 25, 2016 #14
    Well man,I've made a mistake,I forgot to add a voltage/current source in the parallel,my background is very good at electronics,but this doesn't have to do anything with electronics,it's circuit theory.

    This equation is from lecture notes , MIT.

    Okay this picture is from a book 'Linear and non linear electrical circuits',it shows the equation
    http://postimage.org/] odziv.jpg [/PLAIN] [Broken]
    image hosting sites


    And writing down the equation will give me only general solution to the equation,it doesn't say what determines those 3 graphs,it's obvious that initial conditions determine those 3 graphs.And I wasn't upset,I just had a feeling that none understood me.
     
    Last edited by a moderator: May 7, 2017
  16. Jan 25, 2016 #15

    donpacino

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    ok. if you think there is a large difference between electronics and circuit theory, then what is your background in circuit theory.

    developing a mathematical model of the system is very important. from the mathematical model you can see what parameters will effect the outputs in which way. If you have a mathematical model in the frequency domain, you can clearly see the poles and zeros. from there evaluating the poles and zeros will show which parameters will effect the output.

    what is the actual question you are trying to answer? all of it.
    Are you given a circuit? or are you only given graphs?

    If you are given graphs, you can make no assumptions about the circuit, and you need to answer the question mathmatically. where the switch is, and where the sources are will effect the output drastically, if there is even a circuit.
     
    Last edited by a moderator: May 7, 2017
  17. Jan 25, 2016 #16

    donpacino

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    look up dominant zeros.
    it may help you, if you either derive a mathematical expression for the circuit, or don't have a circuit and only need a mathematical answer.
     
  18. Jan 25, 2016 #17
    The professor asked me 'what determines those 3 graphs' that was the question.
     
  19. Jan 25, 2016 #18

    donpacino

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    ok... if that was the entire question, and there is no included or implied circuit, then i would recommend looking up dominant zeros. Or the answer is simply the initial condition
     
  20. Jan 26, 2016 #19
    Sorry I am not native english speaker, what do you mean looking up dominant zeros?
     
  21. Jan 26, 2016 #20

    donpacino

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    have you done any work with transfer functions in the frequency domain?
    do you know what poles or zeros are?

    if you have not worked with the frequency domain this explanation will not be sufficient.

    a dominant zero is when a system has a zero that is smaller or close to the smallest pole of the system.


    http://wolfweb.unr.edu/~fadali/ee370/TimeResp.pdf

    look at the above link. page 4 will kind of explain what poles and zeros are.
    you can see on page 43-46 the effects of the zeros. you should then be able to explain the effects of the graphs you showed above.
     
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