# Forced Damped SHM, AC CLR circuit.

1. Oct 14, 2012

### dannyR

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$\frac{di}{dt}$ + iR +$\frac{q}{C}$= V = V$_{0}$cos(ωt)

solution to this:
I =$\frac{V0}{Z}$ cos(ωt+$\varphi$)

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

so v and I are in phase when $\varphi$=0, when ωL = $\frac{1}{ωC}$

so ω0 = $\frac{1}{\sqrt{LC}}$

f0 =$\frac{1}{2Pi\sqrt{LC}}$

for this experiment L=0.175H stated not verified, C =1$\mu$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