Demonstrate thatat low damping the quality factor `Q` of a circuit maintaining forced oscillations is approximately equal to `omega_(0)//Delta omega`, where `omega_(0)` is the natural oscillation frequency , `Delta omega` is the width of the resonance curve `I(omega)` at the " height " which is `sqrt(2)` times less than the resonance current amplitude.

Explanation

`Q=(omega)/( 2 beta)~~( omega_(0))/( 2 beta)` for low damping.
Now `(I_(m))/( sqrt(2))=(RI_(m))/( sqrt(R^(2)+(omegaL-(1)/( omegaC))^(2))), I_(m)=` current amplitude at resonance
or `omega-(omega_(0)^(2))/( omega)=+- (R)/(L)=+- 2 beta`
Thus ` omega~= omega_(0) +- beta`
So ` Delta omega = 2 beta ` and `Q=(omega_(0))/( Delta omega)`