Determine the value of Q for each of the oscillators

In summary, the conversation is about determining the value of Q for each of the oscillators represented in Figure 1. The Q-value is defined as the rate at which the mass-spring system loses energy to its surroundings, and it can be expressed in terms of angular frequency or frequency. The relation used to estimate Q is Q= (ω/Δω), which represents the width of the peak at its halfway point. The person asking for help is unsure where to start, and the other person responds by asking for an explanation of the relation.
  • #1
Ryan McDonald
19
3

Homework Statement


http://dspace.jorum.ac.uk/xmlui/bitstream/handle/10949/1022/Items/T356_1_030i.jpg

Taking measurements from Figure 1, determine the value of Q for each of the oscillators represented. Explain how you obtained your answer. I haven't made an attempt as answering this as I'm unsure where to start. Any suggestions would be appreciated.

Homework Equations



The rate at which the mass–spring system loses energy to its surroundings is referred
to as the Q-value for the oscillator. The Q-value is defined as:

Q= 2π (E \ ΔE)

ΔE/E is the fractional energy loss per cycle of the oscillation

This can be expressed in terms of angular frequency as:

Q= (ω/ Δω)

or frequency as:

Q= ( f/ Δf)

where Δ ω and Δ f are the width of the peak at its halfway point.
 
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  • #2
Hi Ryan. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Ryan McDonald said:
Q can be expressed in terms of angular frequency as:

Q= (ω/ Δω)
This relation is what you'll use to estimate Q. Can you explain what it's saying?
 
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1. What is the definition of Q for an oscillator?

The quality factor (Q) of an oscillator is a measure of its efficiency and stability. It is defined as the ratio of the energy stored in the oscillator to the energy lost per cycle.

2. How is Q related to the frequency and damping of an oscillator?

Q is inversely proportional to the damping coefficient of an oscillator. This means that a higher Q value corresponds to a lower damping coefficient, allowing the oscillator to oscillate for longer periods of time before dissipating its energy. Q is also directly proportional to the frequency of an oscillator, meaning that a higher Q value corresponds to a higher frequency.

3. Can Q be greater than or equal to 1?

Yes, Q can be greater than or equal to 1. In fact, a higher Q value indicates a more efficient and stable oscillator. A Q value of 1 represents a critically damped oscillator, where the energy is dissipated at the same rate as it is being added. A higher Q value represents an underdamped oscillator, where the energy is dissipated at a slower rate than it is being added.

4. How is Q measured in experimental settings?

Q is typically measured in experimental settings by observing the oscillations of the oscillator and recording the amplitude decay over time. The Q value can then be calculated using the formula Q = 2πf/δf, where f is the resonant frequency and δf is the full width at half maximum (FWHM) of the amplitude decay curve.

5. How does Q affect the response of an oscillator to external forces?

A higher Q value means that an oscillator is more sensitive to external forces at its resonant frequency. This is because a higher Q value corresponds to a sharper resonance peak, which amplifies the amplitude of the oscillator at its resonant frequency. On the other hand, a lower Q value means that an oscillator is less sensitive to external forces and may have a broader resonance peak.

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