3.10 Vibration Measuring Seismic Instruments
87
Fig. 3.17 Variation of Z and φ with η
Plot of η
2
/
( 1 − η 2 ) 2 + (2ηζ )
2 against η for various values of ζ is shown in
Fig. 3.17. Based on Eq. (3.66), two instruments have been developed. They are given
below.
3.10.1 Vibrometer
Vibrometer is an instrument for measuring displacements of the vibrating body. From
Fig. 3.17, it is clear that for η >> 1, η
2
/
( 1 − η 2 ) 2 + ( 2ηζ ) 2 tends to be unity
and the phase angle φ tends to 180°. As such for η >> 1, Eq. (3.66) becomes
z = − y 0 sin ω t
(3.67)
Therefore, the relative displacement directly measures the base displacement,
which in fact is the objective.
To obtain high values of η, the natural frequency of the spring–mass system has
to be of a very low order in comparison with the exciting frequency, preferably onethird to one-half of the lowest frequency to be recorded. In order to obtain a low
natural frequency, the system should have a large mass and soft spring. This will
entail in a large static displacement. Damping is induced in the system to reduce
transient vibrations. The instrument is sensitive and delicate. Vibrometers are rarely
used, other than for seismological measurements.