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dannyR
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Homework Statement
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
Homework 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?
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.
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