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Homework 4
Note
:
The
K
in the equation
0
t/
y(t)
KA (y
KA)e
τ
−
=+−
is not necessarily the same as the
K
for
static sensitivity in
K
=
dy/dx
.
(It is in some cases or if the problem is handled in a certain way,
which is not the way it has been done in the examples you’ve seen so far.
Look at the solutions
when they are posted.)
You may find it easier to consider
11
0
y( t )
K A
( y
K A )e
−
=+
−
and to
find
K
1
A
1
.
1.
Figure 1a shows a temperature sensor response when it is taken from temperature
T
0
=
25.0 °C = 298 Kelvin at time
t
= 0 and put onto an oven at 28.2 °C.
Figure 1b shows the
static calibration curve for this sensor.
51,000
52,000
53,000
54,000
55,000
56,000
57,000
58,000
59,000
60,000
61,000
24
25
26
27
28
29
Temperature (
o
C)
R(T)
51,000
52,000
53,000
54,000
55,000
56,000
57,000
58,000
59,000
60,000
61,000
0
100
200
300
400
500
600
700
800
900
1000
time (msec)
R(t)
a)
(70 pts)
What is the steadystate response of the sensor to an input of
T(t)
=
C
2
+
A
2
sin(
ω
t
), where
= 20 rad/sec,
C
2
= 26 °C,
A
2
= 1.5 °C?
Show your equations, the
values you use, and your calculations.
(Explicitly state any assumptions that you make
in solving this problem and justify the reasonableness or necessity of those
assumptions.)
This system will be modeled as a firstorder system.
First, get
from Figure 1, then use that to obtain the sine response.
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This note was uploaded on 11/28/2010 for the course ENES enes100 taught by Professor Staff during the Spring '10 term at Maryland.
 Spring '10
 staff

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