Page 103 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

90 Harmonically Excited Vibration Chap. 3

Figure P3-41.

3-42 A commercial-type vibration pickup has a natural frequency of 4.75 cps and a damping
factor = 0.65. What is the lowest frequency that can be measured with
(a) 1% error and (b) 2% error?
3-43 An undamped vibration pickup having a natural frequency of 1 cps is used to measure
a harmonic vibration of 4 cps. If the amplitude indicated by the pickup (relative
amplitude between pickup mass and frame) is 0.052 cm, what is the correct amplitude?
3-44 A manufacturer of vibration-measuring instruments gives the following specifications
for one of its vibration pickups:
Frequency range: Velocity response flat from 10 to 1000 cps.
Sensitivity: 0.096 V /c m /s, both volts and velocity in rms values.
Amplitude range: Almost no lower limit to maximum stroke between stops of
0.60 in.
(a) This instrument was used to measure the vibration of a machine with a known
frequency of 30 cps. If a reading of 0.024 V is indicated, determine the rms
amplitude.
(b) Could this instrument be used to measure the vibration of a machine with known
frequency of 12 cps and double amplitude of 0.80 em? Give reasons.
3-45 A vibration pickup has a sensitivity of 40 m V /cm /s from / = 10 to 2000 Hz. If 1 g
acceleration is maintained over this frequency range, what will be the output voltage at
(a) 10 Hz and (b) 2000 Hz?
3-46 Using the equations of harmonic motion, obtain the relationship for the velocity versus
frequency applicable to the velocity pickup.
3-47 A vibration pickup has a sensitivity of 20 m V /cm /s. Assuming that 3 mV (rms) is the
accuracy limit of the instrument, determine the upper frequency limit of the instru­
ment for 1 g exeitation. W hat voltage would be generated at 200 Hz?
^-48 The sensitivity of a eertain crystal accelerometer is given as 18 p C /g , with its
capacitance equal to 450 pF. It is used with a vacuum-tube voltmeter with connecting
cable 5 m long with a capacitance of 50 p F /m . Determ ine its voltage output per g.
1-49 Specific damping capacity W ^/U is defined as the energy loss per cycle divided by
the peak potential energy U = \kX ^. Show that this quantity is equal to

= 477
u ( -
where Î = c/c^^.