Working through my lecture summaries, I have been given that [tex] Q (the quality factor) =\frac{2\pi}{(\Delta E/E)cycle}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

and accepted this as a statement, taking [tex]\((\Delta E/E)cycle}[/tex] to mean the 'energy loss per cycle'.

The notes carry on to say

'The frequency [tex]\widetilde{\omega}[/tex] of under(damped) oscillator as function of the frequency [tex]\omega_{0}[/tex] and the Q factor:

[tex]\widetilde{\omega} = \omega_{0}\sqrt{1 - (\frac{b}{2m\omega_{0})^{2}}} = \omega_{0}\sqrt{1 - \frac{1}{4Q^{2}}[/tex]

My problem being that I cannot prove that [tex]\frac{b}{2m\omega_{0}} = \frac{1}{4Q^{2}} [/tex]

Knowing that [tex]E = E_{0}exp^{-bt/m}[/tex] i tried finding the energy loss per cycle by finding the difference between the energy at time t and the energy at time t + T (where T is the time period) but just ened up with an unhelpfull equation.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Quality Factor in damped oscillation

**Physics Forums | Science Articles, Homework Help, Discussion**