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3 years ago

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An accelerometer has a damping ratio of 0.5 and a natural frequency of 18,000 Hz. It is used to sense the relative displacement

of a beam to which it is attached. (a)If an impact to the beam imparts a vibration at 4500 Hz, calculate the dynamic error and phase shift in the accelerometer output. (b)Calculateits resonance frequency.(c)What isthe maximumpossiblemagnitude ratio that the system can achieve

1 answer:

SOVA2 [1]3 years ago

3 0

Answer:

A) i) Dynamic error ≈ 3.1%

ii) phase shift ≈ -12°

B) 79971.89 rad/s

Explanation:

Given data :

Damping ratio = 0.5

natural frequency = 18,000 Hz

<u>a) Calculate the dynamic error and phase shift in accelerometer output at an impart vibration of 4500 Hz</u>

i) Dynamic error

This can be calculated using magnitude ratio formula attached below is the solution

dynamic error ≈ 3.1%

ii) phase shift

This phase shift can be calculated using frequency dependent phase shift formula

phase shift ≈ -12°

<u>B) Determine resonance frequency </u>

Wr = 2 $\pi$ ( 18000 $\sqrt{0.5}$ ) = 79971.89 rad/s

C) The maximum magnitude ratio that the system can achieve

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