# Extrapolating the Quality factor for decay in amplitudes

1. Sep 17, 2014

### PhysicsKid0123

1. The problem statement, all variables and given/known data
By what factor does the amplitude decay in the time interval (which I had to find).

E: stored energy
γ:damping rate
a: amplitude
t: time
Q: quality factor
T:Period
ω: frequency

2. Relevant equations

Q = 2∏E/(ΔE)

3. The attempt at a solution
I found the interval to be t=QT
but "one cycle" indicates T=2∏?

So I'm not exactly sure if I got the right answer for the quality factor by which the quality factor decays? I feel like there is supposed to be a numerical answer. Any insights? Did I mess up anywhere or took the wrong approach? Anything will help!

Thanks!

#### Attached Files:

File size:
23.8 KB
Views:
71
• ###### 0001.jpg
File size:
19.4 KB
Views:
70
Last edited: Sep 17, 2014
2. Sep 17, 2014

### BvU

Suppose the amplitude decays by a factor of 2 in a certain interval. What does that mean for the stored energy ?

 In fact your answer can be made to look more attractive if you realize that $\omega T = 2\pi$

Last edited: Sep 17, 2014
3. Sep 17, 2014

### PhysicsKid0123

It would lose half of it's stored energy?

Last edited: Sep 17, 2014
4. Sep 17, 2014

Nope.