ME 260 Homework #3
MEASUREMENT TECHNIQUES
March 1, 2007
Dr. B. Zhang
(Instructor)
Office Hours
8:0010:00 (Mon &Wed)
UTE Building, Room 384
and by appointment
Phone: 4862072
[email protected]
1.
A system is modeled by the equation
(
29
t
F
y
y
=
+
. Initially, the output signal is steady at 100 V.
The input signal is suddenly increased to 150 V.
a.
Determine the response equation.
b.
On the same graph, plot both the input signal and the system time response until a steady
response is reached.
FIND
:
y
(
t
)
SOLUTION
:
The solution to the system model was given by the general form,
(
29
(
29
[
]
τ
t
e
y
y
y
t
y

∞
∞

+
=
0
where here,
y
(0)=100 units,
y
∞
=150 units,
and
τ
=1 s.
then,
units
50
150
t
t
e
y


=
Alternatively, by direct solution
)
(
150
t
U
y
y
=
+
for
t
≥
0
+
,
(
29
B
Ce
y
y
t
y
t
p
h
+
=
+
=

By substitution,
B
=150.
Then, if
y
(0)=100,
C
=50.
(
29
t
e
t
y


=
50
150
2.
Suppose a thermometer is known to have a time constant of 50 s in a particular application.
Establish a model that describes its time response to a step change from 32
°
F to 120
°
F.
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 Spring '08
 Zhang
 Harshad number, Step function, Dr. B. Zhang, set threshold value

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