2nd Order Differential Equation RLC

Discussion in 'Homework Help' started by Jvh87, Jul 7, 2009.

  1. Jvh87

    Thread Starter New Member

    Jul 7, 2009
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    Hello,

    Im new here, but I have a problem I have to solve for school. Maybe some of you can help me.
    I have to solve to RLC circuit below in a 2nd order differential equation which is expressed in the variable iL(t)

    [​IMG]

    I have to hand in the answers on friday 12:00h I hope you can help me before then.

    Thanks in advance.

    JvH
     
  2. JoeJester

    AAC Fanatic!

    Apr 26, 2005
    3,373
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    Can you show your work to this point? The purpose of this forum is to help you by pointing out where you may have gone astray with your answers, not do the work for you.
     
  3. Jvh87

    Thread Starter New Member

    Jul 7, 2009
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    Yes, this is what I have so far.

    T<0

    [​IMG]

    A stationary coil behaves as a short circuit. And the capacitor behaves as open terminals, so the power is blocked.

    IL(0-) = 6/3 = 2A (Power chooses the path of least resistance, so run through the short circuit)
    V(0-) = 0V (Short crct)

    T>0

    [​IMG]

    Continuity Conditions coil: IL(0+) = IL(0-) = 2A
    Continuity Conditions capacitor: V(0+) = V(0-) = 0V

    IR(0+) = V(0+)/1 = 0A
    Junction 1: IR + IL+IC = 0 (knp. 1 in the picture)
    ===> IC(0+) = - IL(0+) = -2A

    ---------

    The following laws and formulas have to be applied to the circuit

    Resistance > Ohms law: V(t) = R x I(t) => IR \frac{V(t)}{R}

    Coil > Faradays law: VL(t) = L [​IMG] => \frac{1}{L}V(t)

    Capacitor: Ic = L [​IMG] => IC(t) = C \frac{dV}{dt}

    KCL: [​IMG]Iin = [​IMG]Iout => IR + IL+IC = 0

    This is where I get stuck, how do I get a 2nd order diff. eq. from this bunch of formulas.
     
  4. Ratch

    New Member

    Mar 20, 2007
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    Jvh87,

    The order will be whatever it needs to be to solve the problem. What are you required to solve? Current in each branch, voltage across the branches, what? Are you supposed to set up the differential equation only, or solve it also? You left a lot of guesswork in your request.

    Ratch
     
  5. Jvh87

    Thread Starter New Member

    Jul 7, 2009
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    I only have to set up the diff. eq.
     
  6. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    This might help get you a little further - but it's not the whole story.
     
  7. Jvh87

    Thread Starter New Member

    Jul 7, 2009
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    I get that part, but I have no clue whats next. And the variable has to be IL(t) not V(t). I have to hand it in on friday if I want to graduate in august. So can you explain it further?
    I will look into it and do some studying on the whole diff. eqq. stuff but I just cant get it solved before friday.

    Thanks for the help so far.
     
    Last edited: Jul 8, 2009
  8. Ratch

    New Member

    Mar 20, 2007
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    Jvh87,

    You only answered one of my questions. What are you trying to solve?

    Ratch
     
  9. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    Not to be unkind or pompous Jvh87, but what I gave you was a reasonable starting point. I'd be pleased to reveal more (as would others in the Forum) if you gave some credible feedback on what approach you might take to the solution.
    Given you have stated this work is so pivotal to your graduation you probably need to demonstrate to your teachers (not me by the way) that you are deserving of that reward.
     
  10. Jvh87

    Thread Starter New Member

    Jul 7, 2009
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    I dont have to solve anything I just have to set up the diff. eq.
     
  11. Jvh87

    Thread Starter New Member

    Jul 7, 2009
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    I know that you gave me a reasonable starting point. I just dont know how to procceed further.
    And I dont have to demonstrate it, I just have to hand in the answer with a work-out.

    Thanks for the help so far.
     
  12. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    OK - see if this attachment helps. You'll need to do some work to get there!
     
  13. Ratch

    New Member

    Mar 20, 2007
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    Jvh87,

    The diffy Q for what? The current in one of the branches, the battery current, one of the voltages, what?

    Ratch
     
  14. Jvh87

    Thread Starter New Member

    Jul 7, 2009
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    for iL, current through the inductor
     
  15. Ratch

    New Member

    Mar 20, 2007
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    Jvh87,

    See if this is any help.

    Ratch
     
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