Q factor (Quality Factor)

  • Thread starter theR
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In summary, the amplitude of a driven harmonic oscillator reaches a value of 20.0 F_0 / m at a resonant frequency of 390 Hz.
  • #1
theR
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Homework Statement


The amplitude of a driven harmonic oscillator reaches a value of 20.0 F_0 /m at a resonant frequency of 390 Hz.
What is the Q value of this system?

Since our Professor accidentally gave us the problem set from a different book instead of the one we have, and the one we have makes no mention of Q, the only introduction I have to Q value is a few sentences near the end of class, and it is just confusing me to no end.

Homework Equations


Okay, so as far as I know, Q value is equal to the resonant frequency (w_0) over the width of the resonance. I have several equations relating q to nu (v) and the resonant frequency:

Q = (resonant frequency)/(width of resonance)

Q = (w_0/ v) where v is nu

and

width of resonance at K = Kmax/sqrt(2) = W

The Attempt at a Solution


The main trouble I am having with this problem is trying to figure out how to use the two units given to convert and insert them into the equations I was given. I have assumed that the resonant frequency of 390 Hz was equal to w_0. After this, I have tried several methods to get the final answer:

At first I attempted to insert 390 into w_0 and 20 F_0/m into v and find Q that way.
This resulted in Q = (w_0/v) = 19.5, which was incorrect, and the units are probably off (since Q is unitless)

After this, I tried to use the equation where width = Kmax/sqrt(2). I substituted 20 F_0/m into Kmax and got a width of 14.142 F_0/m. I then substituted this value into the Q equation where: Q = (390 Hz / 14.142 F_0/m) = 27.577, which is incorrect, and again I am pretty sure that my units are off.

After this, I had only two more chances to answer the question so I have just been searching for how to convert the Amplitude given into a width of resonance with no success. Can anybody help me go through the process of converting the two values given into values that I can use in the Q equation?

Thank you to anyone who replies
 
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  • #2
Actually I just figured out another part of the problem. I now think that the units [tex]F_0[/tex] / m are actually values themselves represented by variables.

F0 = maximum driving force

and m is the mass of the object.

This just means that now I think I have to find a way to take this amplitude and plug it into something that gives me the range of resonance frequency values to divide the resonant frequency by. Anyone have any idea how I would go about doing that?
 
  • #3
anybody have any ideas at all?
 

1. What is the definition of Q factor?

The Q factor, also known as the quality factor, is a measure of the quality or efficiency of a resonant circuit. It is defined as the ratio of the energy stored in the circuit to the energy dissipated in one cycle.

2. How is Q factor calculated?

Q factor is calculated by dividing the resonant frequency of a circuit by the bandwidth of the circuit. It can also be calculated by dividing the reactance of the circuit by its resistance.

3. What is the importance of Q factor?

The Q factor is important because it indicates the sharpness of a resonant circuit's response. A higher Q factor means a narrower bandwidth and a more efficient circuit, while a lower Q factor means a wider bandwidth and a less efficient circuit.

4. How does Q factor affect circuit performance?

Q factor affects circuit performance in several ways. A higher Q factor means a circuit will have a higher voltage gain and a narrower bandwidth, making it more suitable for applications where precise frequency control is needed. A lower Q factor means a circuit will have a wider bandwidth and lower voltage gain, making it more suitable for applications where a broad range of frequencies is needed.

5. What factors can affect the Q factor of a circuit?

The Q factor of a circuit can be affected by the quality of its components, the design of the circuit, and external factors such as temperature and humidity. Additionally, parasitic components like resistance, capacitance, and inductance can also affect the Q factor of a circuit.

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