Driven resonance v. natural resonance

In summary, the conversation revolved around a physics lab experiment where a circuit with a 150 milliHenry capacitor and a .5 microfarad capacitor was set up, and the expected resonance frequency was calculated using the natural frequency formula. However, the measured resonance frequency was larger than the expected value, which raised questions about the effect of damping and internal resistance on the results. The conversation also delved into the details of the circuit set up and the calculated and measured values for resonance frequency. The possibility of the lead connections adding inductance to the circuit and the significance of manufacturing tolerances for the capacitance and inductance values were also discussed. Suggestions for further calculations and considerations were given as well.
  • #1
BunmiFariyike
I am in a physics lab course and we set up the following circuit. Given that we had a 150 milliHenry capacitor and a .5 microfarad capacitor, we calculated the expected resonance frequency using the formula for the natural frequency of an LC circuit: omega = 1/ sqrt(LC). We then measured the driven resonance frequency through an oscilloscope. Obviously, the two values should differ slightly because the natural resonance isn't the same as the driven one due to damping from the resistor and the internal resistance of the circuit. However, this should make the driven resonance smaller than the natural one, not larger, right? For all of the measured values, our resonance frequency was larger than what was given by the formula and I need to explain why in my report, but I have researched for hours and genuinely don't know. Can anyone help? Thanks.
 
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  • #2
The 150 mH was for an inductor, correct?
 
  • #3
Were the L and C in series or in parallel? Also, what frequency did you expect to see and what did you measure?
 
  • #4
magoo said:
Were the L and C in series or in parallel? Also, what frequency did you expect to see and what did you measure?
My apologies. I thought the picture of the circuit would display. L and C were in series. We tested 3 different resonance values: 10, 50, and 500 ohms and I obtained values for angular frequency of 3727, 4242, and 3759, respectively. The expected value was 3651.48. Thank you.
 
  • #5
I didn't see any picture with what you submitted. Normally I would calculate the frequenct - f - rather than omega. This will give you 581.2 hertz.

By calculating the frequency, the result is a smaller result so the 3 test values will appear closer. Percentagewise, they will be the same.
 
  • #6
One additional item to consider is the lead connections in your test circuit. They add some inductance - like about 0.4 mH /ft of lead length. With 5 ft of lead, you'd have 2 mH of inductance added to what you already had. This factor is often used by lightning or surge protection engineers.

2 mH isn't much, but it will change your calculated angular frequency to 3627.4.
 
  • #7
Did you measure the inductance and capacitance or rely on the nominal value? They can have significant manufacturing tolerances.
 
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1. What is the difference between driven resonance and natural resonance?

Driven resonance refers to a phenomenon in which an external force or frequency is applied to a system, causing it to vibrate at a specific frequency. Natural resonance, on the other hand, occurs when a system vibrates at its own natural frequency without any external forces.

2. How do driven resonance and natural resonance affect the behavior of a system?

Driven resonance can cause a system to vibrate at a higher amplitude than its natural frequency, leading to potential damage or failure. Natural resonance can also cause a system to vibrate at high amplitudes, but this is typically not a concern as the system is designed to withstand its own natural frequency.

3. What are some examples of systems that exhibit driven resonance?

Examples of systems that exhibit driven resonance include musical instruments, structures such as bridges and buildings, and electronic circuits. In each of these cases, an external force or frequency is applied to the system to produce a desired response.

4. Can driven resonance and natural resonance occur simultaneously in a system?

Yes, it is possible for a system to experience both driven resonance and natural resonance at the same time. This can happen when an external force is applied to a system that is already vibrating at its natural frequency, leading to a combination of the two types of resonance.

5. How can driven resonance and natural resonance be controlled or prevented?

To prevent or control driven resonance, engineers can design systems with dampeners or absorbers to reduce the effects of external forces. Natural resonance can be controlled by avoiding the system's natural frequency or by modifying the system's design to change its natural frequency.

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