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 = (\omega_0)/(\Delta \omega)`

`Q = (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 = (2\pi*1.40)/(2\pi*0.021)`

so we have

`Q = 66.67`

So quality factor of given AC is 66.67