Fourier transform problem

Discussion in 'Math' started by dhammikai, Nov 25, 2009.

  1. dhammikai

    Thread Starter New Member

    Sep 12, 2009
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    Hi, I am following a course of Mathematics, I got a problem as my home work as follows; Please give me a help to fing out the answer for following RLC problem.

    An R.L.C. circuit has an emf of 100 cos2t, a resistance of 80Ω, an inductance of 20H and capacitance of 10^-2 F. Find an expression for the charge at any time t.
     
    Last edited: Nov 25, 2009
  2. Nanophotonics

    Active Member

    Apr 2, 2009
    365
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    Are you sure it's a fourier transform problem? Are the components in series?
     
  3. dhammikai

    Thread Starter New Member

    Sep 12, 2009
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    Hi thanks for the reply:),
    actually this my home work is include in the Fourier series class, if there any other path is available for answer this qustion please let me know (differentiating or ..). The question is not directly print as these are in series. but normally these are in series.
     
    Last edited: Nov 25, 2009
  4. Nanophotonics

    Active Member

    Apr 2, 2009
    365
    3
    OK, if they are in series, then you should be able to find an expression like this :-

    Voltage source = Voltage across resistor + voltage across capacitor + voltage across inductor

    Try to express this in terms of charge at any time t. Yes, you can use calculus.
     
  5. dhammikai

    Thread Starter New Member

    Sep 12, 2009
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    OK Thank you very much Nanophotonics, I gut an idea for the answer now. Thank you very much:):)
     
  6. steinar96

    Active Member

    Apr 18, 2009
    239
    4
    The RLC circuit is characterised by a second order differential equation. If you manage to get the differential equation right, and IF the condition of inital rest applies (y = 0 for x<0, meaning it is a linear time invariant system, and since it's BIBO stable (bounded input bounded output)) the laplace transform will converge on the jω axis meaning that the fourier transform does exist.... then you can apply the fourier transform on the differential equation and solve it.

    If it has nonzero inital conditions you need to use the laplace transformation. But since you're in a fourier course then i assume the conditions above apply.
     
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