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design of the characteristics of this spring-mass-damper system, the output is a direct indication of
either displacement or acceleration. To accomplish a specific measurement, this basic seismic
transducer is rigidly attached to the object experiencing the motion that is to be measured.
Consider the case where the output transducer senses the position of the seismic mass; a variety
of transducers could serve this function. Under some conditions, the displacement of the seismic
mass serves as a direct measure of the acceleration of the housing and the object to which it is
attached. To illustrate the relation between the relative displacement of the seismic mass and
acceleration, consider the case in which the input to the seismic instrument is a constant
acceleration. The response of the instrument is illustrated in Figure 12.8. At steady-state conditions,
under this constant acceleration, the mass is at rest with respect to the housing. The spring deflects an
amount proportional to the force required to accelerate the seismic mass, and since the mass is
known, Newton’s second law yields the corresponding acceleration. The relationship between a
constant acceleration and the displacement of the seismic mass is linear for a linear spring (where
F ¼ kx).
We might want to measure not only constant accelerations but also complex acceleration
waveforms. Recall from Chapter 2 that a complex waveform can be represented as a series of sine or
Spring
Object
in motion
Output
transducer
Seismic
mass
Damper
Input
motion
M
Figure 12.7 Seismic transducer.
Spring force
Acceleration
direction
Position under
constant acceleration
Constant acceleration
magnitude
Linear
spring
Position of
seismic mass
Output
displacement
x
Rest position
Figure 12.8 Response of a seismic transducer to a constant acceleration.
12.2 Sensors 511
13:54:9 Page 511
design of the characteristics of this spring-mass-damper system, the output is a direct indication of
either displacement or acceleration. To accomplish a specific measurement, this basic seismic
transducer is rigidly attached to the object experiencing the motion that is to be measured.
Consider the case where the output transducer senses the position of the seismic mass; a variety
of transducers could serve this function. Under some conditions, the displacement of the seismic
mass serves as a direct measure of the acceleration of the housing and the object to which it is
attached. To illustrate the relation between the relative displacement of the seismic mass and
acceleration, consider the case in which the input to the seismic instrument is a constant
acceleration. The response of the instrument is illustrated in Figure 12.8. At steady-state conditions,
under this constant acceleration, the mass is at rest with respect to the housing. The spring deflects an
amount proportional to the force required to accelerate the seismic mass, and since the mass is
known, Newton’s second law yields the corresponding acceleration. The relationship between a
constant acceleration and the displacement of the seismic mass is linear for a linear spring (where
F ¼ kx).
We might want to measure not only constant accelerations but also complex acceleration
waveforms. Recall from Chapter 2 that a complex waveform can be represented as a series of sine or
Spring
Object
in motion
Output
transducer
Seismic
mass
Damper
Input
motion
M
Figure 12.7 Seismic transducer.
Spring force
Acceleration
direction
Position under
constant acceleration
Constant acceleration
magnitude
Linear
spring
Position of
seismic mass
Output
displacement
x
Rest position
Figure 12.8 Response of a seismic transducer to a constant acceleration.
12.2 Sensors 511