Extrapolating the Quality factor for decay in amplitudes

[PhysicsKid0123]

Homework Statement

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

Homework Equations

Q = 2∏E/(ΔE)

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!

 

[BvU]

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

Vice versa yields your answer without much effort !

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

 

[PhysicsKid0123]

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

Vice versa yields your answer without much effort !

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

It would lose half of it's stored energy?

 

[BvU]

Nope.