for a vibrometer has a period of free vibrations of 3 seconds. it is attached to a machine with a vertical harmonic frequency of 2hz. if the vibrator mass has an amplitude of 1.5mm relative to the vibrometer frame what is the amplitude of vibration of machine
Answers
Answer:Introduction to Mechanical Vibration (NOC-17 ME-08)
Assignment: 05: Vibration Measuring Instruments
Q.01 A vibrometer having a natural frequency of 4 rad/s and ξ=0.3 is attached to a structure that
performs a harmonic motion. If the difference between the maximum and the minimum
recorded values is 8 mm, find the amplitude of motion of the vibrating structure when its
frequency is 44 rad/s.
(a) 3.82 mm (b) 3.90 mm (c) 3.97 mm (d) 4.05 mm
Q.02. A spring-mass system with m=0.5 kg and k=10,000 N/m with negligible damping, is used
as a vibration pickup. When mounted on a structure vibrating with an amplitude of 4 mm,
the total displacement of the mass of the pickup is observed to be 12 mm. Find the frequency
of the vibrating structure.
(a) 12.5 Hz (b) 18.4 Hz (c) 22.7 Hz (d) 26.2 Hz
Q.03 A vibration pickup has been designed for operation above a frequency level of 100 Hz
without exceeding an error of 2 percent. When mounted on a structure vibrating at a
frequency of 100 Hz, the relative amplitude of the mass is found to be 1 mm. Find the
suspended mass of the pickup if the stiffness of the spring is 4000 N/m and damping is
negligible.
(a) 0.52 kg (b) 1.12 kg (c) 1.68 kg (d) 2.12 kg
Q.04 Design a velometer if the error is to be limited to 1 percent of the true velocity. The natural
frequency of the velometer, which is used to measure the velocity of machine operating at
226 Hz, is to be 80 Hz and the suspended mass is to be 0.05 kg
(a) k = 12633 N/m, c = 32.9 N-s/m (b) k = 15600 N/m, c = 22.3 N-s/m
(c) k = 18500 N/m, c = 32.9 N-s/m (d) k = 21600 N/m, c = 22.3 N-s/m
Q.05 What is the smallest natural frequency of an accelerometer of damping ratio 0.2 that measures
to vibrations of a body vibrating at 200 Hz with an error of a 2 percent?
(a) 1090 Hz (b) 1370 Hz (c) 1560 Hz (d) 1830 Hz
Q.06. An accelerometer is used to measure the oscillation of an airplane wing caused by the plane’s
engine operating at 6000 rpm. At this engine speed the wing is known, from other
measurements, to experience 1.0-g acceleration. The accelerometer measures an acceleration
of 10 m/s2
. If the accelerometer has a 0.01-kg moving mass and a damped natural frequency
of 100 Hz, then calculate the damping ratio and stiffness parameters associated with the
accelerometer.
(a) k= 3625.8 N/m, ξ= 0.36 (b) k= 4526.6 N/m, ξ= 0.42
(c) k= 5060.2 N/m, ξ= 0.47 (d) k= 5751.5 N/m, ξ= 0.56
Q.07. A seismic instrument with a natural frequency of 6 Hz is used to measure the vibratio0n of
a machine operating at 120 rpm. The relative displacement of seismic mass as read from the
instrument is 0.05 mm. determine the amplitude of vibration of the machine. Neglect
damping.
(a) 0.105 mm (b) 0.206 mm (c) 0.305 mm (d) 0.409 mm
Q.08. A spring-mass system, having a static deflection of 10 mm and negligible damping, is used
as a vibrometer. When mounted on a machine operating at 4000 rpm, the relative amplitude
is recorded as 1 mm. Find the maximum values of velocity of the machine.
(a) 25.55 cm/s (b) 32.65 cm/s (c) 41.65 cm/s (d) 52.3 cm/s
Q. 09.A vibrometer having the amplitude of vibration of the machine part as 4 mm and ξ=0.2,
performs harmonic motion. If the difference between the maximum and minimum recorded
value is 10 mm, determine the natural frequency of vibrometer if the frequency of the
vibration part is 12 rad/sec.
(a) 3.55 rad/s (b) 5.66 rad/s (c) 7.56 rad/s cm/s (d) 10.2 rad/s
Q.10. For measuringthe frequency of vibration of a system, a Frahm’s Reed Tachometer is to be
designed. A mass of 0.01 kg is to be placed at the end of one of the reeds so that the reed is
in resonance at a frequency of 15 Hz. The steel reed is 40 mm long and 3 mm wide.
Determine the length of the reed . Take E= 2x 1011 N/m2
.
(a) 1.112 mm (b) 0.786 mm (c) 0.336 mm (d) 0.122 mm
Key of Assignment 5
Q. No. 01 02 03 04 05 06 07 08 09 10
marks
option c b a a b d d c b c
Explanation: