Calculate the highest frequency:

An accelerometer is made along a crystal of natural frequency 20 k Hz. The damping of the accelerometer is equal to 0.6. Calculate the highest frequency at which accelerometer may be utilized with 1% accuracy.

Solution

It is given that

Natural frequency f_n = 20 k Hz

ζ = 0.7

Accuracy = 1%

The function specified in Equation (4) takes care of accuracy in the accelerometer

f = 1 - 0.01 = 0.99

0.9801 {(1 - 2r ² + r ⁴) + 4 × (0.7)² r ²} = 1

Or   r ⁴ - 0.04r ² + 1 = 1.02

Or r ^{4 -} 0.04r ² - 0.02 = 0

It gives the following,

r = 0.428

r = ω/ ω_n =   f/ f_n

∴ f = 0.428 × 20 = 8.56 k Hz