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ME 365
HOMEWORK SET 6
Spring 2010
Out: Thursday, February 25 2010
Due: Thursday, March 4 2010
1
Solve each problem on separate sets of sheets.
Dynamic System Response—Frequency Response
Problem
1 (First Order Frequency Response)
The time response of a thermocouple is described by the following first order differential equation:
dy
y
KT
dt
where y is the output voltage, T is the input temperature,
is the time constant, K is the static
sensitivity, and V
0
is the bias voltage.
a.
Write the frequency response function of the thermocouple and its magnitude and phase or
argument as a function of angular frequency.
b.
For
=2 seconds, K=0.001V/
C, T
0
=25
C, write the particular solutions for environmental
temperatures following the following functions:
i.
T=25+3sin2πt
C
ii.
T=25+3cos2πt
C
iii.
T=25+3cos2πt+3sin2πt+2cos6πt+2sin6πt+cos10πt+sin10πt
iv.
T=25+3cos(2πt+10
)+4sin(2πt+50
)
c.
Plot all of the input temperatures and voltage responses in part (b) for a time period of 10
seconds using MATLAB. Do this is a single plot with two subplots in MATLAB—with the input
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 Spring '08
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