Forced Damped SHM, AC CLR circuit.

In summary, the conversation discusses an experiment on forced damped simple harmonic motion using a CLR circuit to measure the resonance frequency of the system. The solution involves calculating the phase angle and determining when voltage and current are in phase. The expected value for the resonance frequency is around 380 Hz, but the experiment yielded a value of 392±1 Hz. Possible sources of error include measurement errors, defects in circuit components, environmental factors, or issues with the experimental setup. It is recommended to double check calculations and equations and repeat the experiment multiple times to obtain consistent results.
  • #1
dannyR
8
0

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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  • #2


Hello, it sounds like you have done a thorough experiment and have obtained consistent results. However, it is possible that there are some systematic errors present that are causing your results to be slightly off from the expected value of 380 Hz. Here are some potential sources of error to consider:

1. Measurement errors: Even small errors in your voltage and frequency measurements can add up and affect your final result. Make sure to double check your measurements and use the most precise instruments available.

2. Circuit components: As you mentioned, there could be a small defect in your inductor that is affecting your results. It is also possible that the capacitor or resistor have some imperfections that are causing slight deviations from the expected values. You may want to try using different components or calibrating them before conducting the experiment.

3. Environmental factors: External factors such as temperature and humidity can also affect the performance of your circuit components. Make sure to conduct your experiment in a controlled environment and take note of any changes in temperature or humidity.

4. Experimental setup: It is possible that there may be some issues with your experimental setup that are causing errors. Make sure all connections are secure and that there are no loose or damaged wires.

I would also recommend double checking your calculations and equations to ensure that there are no errors there. If all else fails, it may be helpful to repeat the experiment multiple times to see if you consistently obtain the same results. If your results are consistently off from the expected value, it may be worth considering if there are any issues with the stated values of the components or if there is a need for further calibration. Good luck!
 

1. What is Forced Damped SHM?

Forced Damped SHM (Simple Harmonic Motion) is a type of motion that occurs when a damped harmonic oscillator is subjected to an external force. It is characterized by the oscillation of a system around an equilibrium point with a decreasing amplitude over time due to the presence of damping.

2. What factors affect the amplitude and frequency of Forced Damped SHM?

The amplitude and frequency of Forced Damped SHM are affected by the damping coefficient, the stiffness of the system, and the amplitude of the external force. An increase in damping or stiffness will decrease the amplitude and increase the frequency, while an increase in the external force will increase the amplitude and frequency.

3. How does AC CLR circuit relate to Forced Damped SHM?

An AC CLR (capacitor-inductor-resistor) circuit is an electrical circuit that exhibits Forced Damped SHM. The capacitor and inductor in the circuit act as the mass and spring in a mechanical oscillator, while the resistance provides damping. Thus, the behavior of an AC CLR circuit is analogous to that of a forced damped harmonic oscillator.

4. What is the importance of studying Forced Damped SHM and AC CLR circuits?

Forced Damped SHM and AC CLR circuits have applications in various fields such as engineering, physics, and electronics. Understanding these systems can help in designing and analyzing mechanical and electrical oscillatory systems, such as bridges, buildings, and electronic circuits.

5. How is energy dissipated in a Forced Damped SHM system?

In a Forced Damped SHM system, energy is dissipated through the damping force, which is typically in the form of friction. As the system oscillates, energy is lost due to friction between the moving parts, resulting in a decrease in amplitude over time. This dissipation of energy is what causes the oscillations to eventually cease.

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