Solving systems of differential equations - from Kirchhoff's law

Discussion in 'Math' started by Motanache, Mar 3, 2015.

  1. Motanache

    Thread Starter Member

    Mar 2, 2015
    70
    4
    Kirchoff law is so clear, that we can write for the variable current.
     
  2. Motanache

    Thread Starter Member

    Mar 2, 2015
    70
    4
    Last edited: Mar 3, 2015
  3. Motanache

    Thread Starter Member

    Mar 2, 2015
    70
    4
    For this circuit we write equations and we obtain a system of equations.
    How to solve that system of equations ?

    The circuit from below Figure,
    The signal generator provides exponential form.

    The current through Radd is required.
    Any answer, or any suggestion are welcome.
    But wish no offense for other members of the discussion.
     
    Last edited: Mar 3, 2015
  4. WBahn

    Moderator

    Mar 31, 2012
    17,716
    4,788
    In order to solve the system of equations, you first have to obtain the system of equations to be solved. Have you done this? If so, what did you get?

    Then you can solve them using any valid technique to solve a system of differential equations and there are several. For the systems of equations that result from the analysis of linear systems, the use of Laplace transforms and very common and powerful.
     
  5. Motanache

    Thread Starter Member

    Mar 2, 2015
    70
    4
    Obvious.

    I do not think I took a good example. If I was not wrong at calculations, the problem is easy to solve.
    But I have seen cases in which even with eigenvectors method I could not solve them.:(

    CodeCogsEqn1.gif
    CodeCogsEqn2.gif
    CodeCogsEqn3.gif
    CodeCogsEqn4.gif
    CodeCogsEqn5.gif
    CodeCogsEqn6.gif
    CodeCogsEqn7.gif CodeCogsEqn8.gif CodeCogsEqn9.gif
    Free online Wolfram Mathematica for the final equation:
    http://www.wolframalpha.com/input/?i=f*y'' + g*y'+h*y = a*b*Exp(b*x)
     
    Last edited: Mar 4, 2015
  6. Motanache

    Thread Starter Member

    Mar 2, 2015
    70
    4
    http://en.wikipedia.org/wiki/RLC_circuit

    Another question?

    How they achieved bandwidth (implicitly Q Factor)?
    It can be mathematically demonstrate the bandwidth?
    Why the bandwidth (through Q Factor) depend on reactive power divided by active power?

    When I think of bandwidth, I imagine the voltage function FFT.
     
    Last edited: Mar 5, 2015
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