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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.

Sagot :

Answer:

Explanation:

Given:

Q factor, =1000

natural frequency, [tex]f_n=2000~Hz[/tex]

Damping factor, [tex]\zeta=?[/tex]

Bandwidth, BW=?

We have the relation:

[tex]Q=\frac{1}{2\zeta}[/tex]

[tex]\zeta=\frac{1}{2Q}[/tex]

[tex]\zeta=\frac{1}{2\times 1000}[/tex]

[tex]\zeta=5\times 10^{-4}[/tex]

Bandwidth:

[tex]BW=\frac{f_n}{Q}[/tex]

[tex]BW=\frac{2000}{1000}[/tex]

[tex]BW=2~Hz[/tex]

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