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Forced Damped SHM, AC CLR circuit.

  1. Oct 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Hello, I've recently finished an experiment on forced damped simple harmonic motion with a CLR "capacitor , inductor, resistor" circuit with the aim to measure the resonance frequency of the system, using a family of graphs for which each the resistance is varied.

    voltages in series CLR circuit:
    L[itex]\frac{di}{dt}[/itex] + iR +[itex]\frac{q}{C}[/itex]= V = V[itex]_{0}[/itex]cos(ωt)

    solution to this:
    I =[itex]\frac{V0}{Z}[/itex] cos(ωt+[itex]\varphi[/itex])

    phase angle is then given by:
    tan([itex]\varphi[/itex]) = [itex]\frac{ωL-\frac{1}{ωC}}{R}[/itex]

    so v and I are in phase when [itex]\varphi[/itex]=0, when ωL = [itex]\frac{1}{ωC}[/itex]

    so ω0 = [itex]\frac{1}{\sqrt{LC}}[/itex]

    f0 =[itex]\frac{1}{2Pi\sqrt{LC}}[/itex]

    for this experiment L=0.175H stated not verified, C =1[itex]\mu[/itex]F, R was varied from 10 - 600 ohms to obtain a family of curves.

    Experimental method:
    Voltage from AC source was set to 1V and monitored for all readings
    measured voltage across capacitor
    measured voltage across resistor
    changed frequency repeat above steps several times
    increase R repeat above

    Graphed Vc / f
    Graphed current through resistor / f

    2. Relevant equations

    So where I'm stuck, is from my data to obtain f0 it's about 392±1 Hz
    and all my data is consistent that f0 should be above 380 Hz
    from the derivation and stated values of C and L it should be around 380Hz

    during the experiment my errors were very small affecting the 3rd significant figure.

    could this be systematic errors?
    stated values of L and C are wrong slightly?


    3. The attempt at a solution

    I have done some research and it could be possible to have a small defect within inductor, chances are it is a old component. Maybe there is a source of systematic error but I find this hard since experimentally I was only reading volt meters.

    So I'm after a bit of new perspective, I'm sure that I have over looked something and would be grateful for your help.


    Sorry I'm a physics a math's undergrad at university, but looking at the complexity of other problems in the Advanced section, this might need to be moved. My apologies.
     
    Last edited: Oct 14, 2012
  2. jcsd
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