Question

An accelerometer is measuring a structure as described below: Damping ratio of accelerometer = 0.65 Highest frequency measured by the accelerometer = 6000 hz Natural frequency of the accelerometer = 18000 hz What is the percentage error in the accelerometer at the highest frequency it can measure? (Type in a two-decimal number that represents a percentage)

Answer 1

For finding the error in measurement we can find, $\zeta=0.65$ ,$f=6,000,f_n= 18,000$

$E+1 =\frac{1}{(1-\frac{\omega}{\omega_n}^2)^2} + (\frac{2 \zeta \omega }{\omega_n})^2$

$E+1 =\frac{1}{(1-\frac{6000}{18000}^2)^2} + (\frac{2 \times 0.65 \times 6000 }{18000})^2$

E+1 = 1.2656 + 0.1877

E= 0.4533

E= $45.33$ % this is the error percentage