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Damped ocillator LCR circuit

  1. Oct 10, 2014 #1
    1. The problem statement, all variables and given/known data
    Damped oscillator.PNG

    2. Relevant equations


    3. The attempt at a solution

    For part (a) i did the following;
    the time for it to decay to 40% is half the period of the square wave = 0.00002 seconds
    So, 0.4qm = qm ## e^(\frac{-0.00002R}{2L})cos(25000*2*\pi*0.00002) ##
    But the cosine term yields -1 which then makes the equation unsolvable, what am i doing wrong?

    For part (b) im a bit confused about the "17 ringing cylcles per half-cycle" but i tried ;

    the time for one half oscillation of the square wave voltage is 0.5/(25E3) = 0.00002 seconds
    during this time the LCR circuit rings 17 times so the period of oscillation of the LCR circuit is 0.00002/17 = 0.000001176
    this corresponds to an angular freq of w = 5340707.511 rad.s^-1
    Is this correct so far? and if so, does this mean there will be a different restance in part (b) than in part (a)?
     
  2. jcsd
  3. Oct 10, 2014 #2

    NascentOxygen

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    Staff: Mentor

    Don't involve the cosine. For the decay all we are concerned with is the exponential envelope.
     
  4. Oct 10, 2014 #3
    Thank you, I should have realised that.
    Do you know if what i did for part (b) is correct?
     
  5. Oct 10, 2014 #4

    NascentOxygen

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    Staff: Mentor

    Your ##\mathrm{\omega}## looks right. You cannot estimate R from ##\textrm{ω}## because you don't know ##\mathbf{ω}## to the great precision necessary. The exponential decay is what allows you to determine R.
     
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