The vibrations of an engine mount are to be monitored by an accelerometer which can be treated as a second-order system. It is expected that the vibrations will not exceed 1 kHz.
SHOW ALL DERIVATIONS OR EXPLAIN YOUR ANSWER IN PARTS (i) AND (iii)
(i) If you have an accelerometer that has a ringing frequency of 20 kHz and if you want to satisfy the ±3 dB transmission band requirement, do you think that such an accelerometer can be used? Justify your answer with some math.
(ii) If you decide that the above accelerometer is overkill and you want to use an accelerometer that has a ringing frequency of 1.5 kHz, estimate the damping ratio that will allow you to satisfy the ±3 dB transmission band. Show the math.
(iii) Since in reality, the vibrations do not just “magically” die off at 1 kHz, what must you do to get rid of anything above 1 kHz. If you were to sample the data, what is your sampling rate? Is the sampling rate affected by the transducer’s undammed natural frequency (yes or no will suffice)? An explanation in words is enough.