7. An accelerometer is to be used to sense the vibrations of the rollers in a ro

Question

7. An accelerometer is to be used to sense the vibrations of the rollers in a rolling setup. If the accelerometer can be considered as an undamped second-order system with inertia 0.05 Kg and stiffness 1250 N/mm: a) What is the accelerometer's natural frequency? b) Determine the range of fr equencies (for sinusoidal inputs) over which the accelerometer output does not change more than 15% from that corresponding to a static input of the same magnitude. This shows why periodic inputs at frequencies approaching the accelerometer's natural frequency render it useless.

Explanation / Answer

a)given data

Stiffness(k)=1250N/mm

=1250*1000N/m

& Load(m)=.05 kg

Natural frequecy is given as=(k/m)^(1/2)

=(1250*1000/.05)^(1/2)

=5000 rad/seconds

asit doesnt go beyond 15% i.e

it can change only by=0.15*5000=750rad/seconds

hence upper limit =5000 rad/seconds

and lower limit =5000-750=4250 rad/seconds

Rnge(5000,4250)rad/seconds

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