Question

A micromechanical resonator is to be designed to have a Q factor of 1000 and a natural frequency of 2 kHz. Determine the system-damping factor and the system bandwidth.

Answer 1

Step-by-step explanation:

Given:

Q factor, =1000

natural frequency,
`f_n=2000~Hz`

Damping factor,
`\zeta=?`

Bandwidth, BW=?

We have the relation:

`Q=(1)/(2\zeta)`

`\zeta=(1)/(2Q)`

`\zeta=(1)/(2* 1000)`

`\zeta=5* 10^(-4)`

Bandwidth:

`BW=(f_n)/(Q)`

`BW=(2000)/(1000)`

`BW=2~Hz`