Question

A mass and spring system has a resonance at f0 = 1.40 hz with a full-width of ffw = 0.021 hz. what is the quality factor q?

Answer 1

Quality Factor is defined as the ratio of Resonance frequency per unit band width

it is given as

$Q = \frac{\omega_0}{\Delta \omega}$

$Q = \frac{2\pi f_0}{2\pi f_{fw}}$

now here it is given that

$f_0 = 1.40 hz$

$f_{fw} = 0.021 hz$

now we have

$Q = \frac{2\pi*1.40}{2\pi*0.021}$

so we have

$Q = 66.67$

So quality factor of given AC is 66.67