E1C03 09/14/2010
15:24:53 Page 99
SOLUTION A comparison between the governing equation for the accelerometer in Example
3.1 and Equation 3.13 gives
v n ¼
ffiffiffiffi
k
m
r
z ¼
c
2
ffiffiffiffiffiffi ffi
km
p
Accordingly, the physical parameters of mass, spring stiffness, and frictional damping control the
natural frequency and damping ratio of this measurement system.
Example 3.8
The curve shown in Figure 3.15 is the recorded voltage output signal of a diaphragm pressure
transducer subjected to a step change in input. From a static calibration, the pressure–voltage
relationship was found to be linear over the range 1 atmosphere (atm) to 4 atm with a static
sensitivity of 1 V/atm. For the step test, the initial pressure was atmospheric pressure, p a , and the
final pressure was 2p a . Estimate the rise time, the settling time, and the ringing frequency of this
measurement system.
KNOWN p 0
ð Þ ¼ 1 atm
p 1 ¼ 2 atm
K ¼ 1 V=atm
0.00
0.01
0.0038
0.009
0.02
Time, t (s)
Damped
oscillations
Steady response
0.03
0.04
0.05
Output signal
E(t) [V]
0
1
1.9
2
3
Settling
time
(±10%)
90%
Rise
time
T d
0.013 S
Figure 3.15 Pressure transducer time response to a step input for Example 3.8.
3.3 Special Cases of the General System Model 99
15:24:53 Page 99
SOLUTION A comparison between the governing equation for the accelerometer in Example
3.1 and Equation 3.13 gives
v n ¼
ffiffiffiffi
k
m
r
z ¼
c
2
ffiffiffiffiffiffi ffi
km
p
Accordingly, the physical parameters of mass, spring stiffness, and frictional damping control the
natural frequency and damping ratio of this measurement system.
Example 3.8
The curve shown in Figure 3.15 is the recorded voltage output signal of a diaphragm pressure
transducer subjected to a step change in input. From a static calibration, the pressure–voltage
relationship was found to be linear over the range 1 atmosphere (atm) to 4 atm with a static
sensitivity of 1 V/atm. For the step test, the initial pressure was atmospheric pressure, p a , and the
final pressure was 2p a . Estimate the rise time, the settling time, and the ringing frequency of this
measurement system.
KNOWN p 0
ð Þ ¼ 1 atm
p 1 ¼ 2 atm
K ¼ 1 V=atm
0.00
0.01
0.0038
0.009
0.02
Time, t (s)
Damped
oscillations
Steady response
0.03
0.04
0.05
Output signal
E(t) [V]
0
1
1.9
2
3
Settling
time
(±10%)
90%
Rise
time
T d
0.013 S
Figure 3.15 Pressure transducer time response to a step input for Example 3.8.
3.3 Special Cases of the General System Model 99