Mechanical Vibrations
Tutorial-III
1)
A vibrometer has an undamped natural frequency of
10 Hz and a damped natural frequency of 8 Hz. Find the
lowest frequency in the range to infinity at which the
amplitude can be directly read from the vibrometer with
less than 2 percent error.
2)
A spring mass damper system, having an undamped
natural frequency of 100 Hz and a damping constant of 20
N-s/m, is used as an accelerometer to measure the
vibration of a machine operating at a speed of 3000 rpm.
If the actual acceleration is 10 𝑚/𝑠 2 and the recorded
acceleration is 9 𝑚/𝑠 2 , find the mass and spring constant
of accelerometer.
3)
A seismic instrument is mounted on machine at 1000
rpm the natural frequency of seismic instrument is 20
rad/sec. The instruments record relative amplitude of 0.5
mm. Compute displacement, velocity and acceleration of
machine. Damping of seismic instrument is neglected.
4)
An accelerometer of natural frequency 200 Hz and
damping ratio 0.7 is used to measure the vibrations of a
system whose actual displacement is 𝑦(𝑡) =
[1.6 sin(45.1) 𝑡] mm. What is the output of
accelerometer?
5)
A vibrometer is used to measure the vibration at the
base of a variable speed machine. The operating speed of
machine ranges between 500 to 1500 rpm. It is desired to
keep the amplitude distortion at more than 4 % Determine
the natural frequency of vibrometer if damping factor is
0.6.
6)
An accelerometer has natural frequency 15 KHz,
determine the highest frequency it can measured within 1
% accuracy. Assume damping ratio 0.7.
7)
A commercial type vibration pick up has a natural
frequency of 5.75 Hz and a damping factor of 0.65, what
is the lowest frequency beyond which the amplitude can
be measured within 2 percent error.
8)
Determine the necessary stiffness and damping
constant of an accelerometer. If the maximum error is to
be limited to 3 percent for measurements in the frequency
range of 0 to 100 Hz. Assume that the suspended mass is
0.05 kg.
9)
Determine the maximum percent error of a
vibrometer in the frequency ratio of 4 with a damping ratio
of 0 and 0.69
10)
An accelerometer has a suspended mass of 1.01 kg
with a damped natural frequency of vibration is 160 Hz
when mounted on an engine undergoing an acceleration of
9.81 𝑚/𝑠 2 by the instrument. Find the damping constant
and the spring stiffness of the accelerometer. Assume
recorded acceleration as 9.6 𝑚/𝑠 2 when speed is 5000
rpm.