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Name ___________________________
EM
Examination II
October 9, 2001
Problem Score
Total /
This is an closed book/closed note exam with the following conditions.
1. You are allowed a maximum of 3 hours to take the exam
2. The exam must by completed at one sitting
3. You may only use your crib sheet, existing Maple worksheets and Matlab
Simulink models.
4. You are not to discuss the exam with ANYONE!
Show all work for credit
AND
Turn in your signed help sheet
Honor Statement: I pledge my honor that I neither gave nor received help on this
exam, and I only worked on the test during the time allotted.
Signed
Start time ________ End __________
This is a take home, closed notes,
closed book and closed neighbor
exam. You may use the one crib
sheet that you prepared prior to
the exam and any existing Matlab
Simulink models and Maple
worksheets you developed for this
class.
You have three hours to work on
this exam (it shouldn’t take this
long, but I don’t want time to be a
factor.
Do not talk to anyone else in the
class about the exam prior to the
time it is due.
Show all work for credit. If you
use Maple or Matlab, staple a
printout to the exam.
Turn in the signed crib sheet
You will be required to sign an
honor statement and indicate the
times you worked on the exam.
The test is due at 5:00 PM on
Wednesday.
EM406 Examination II Problem 2 October 9, 2001
A second order system (m = 10 kg, k = 100,000 N/m, c = 200 N-s/m) is forced with a periodic input as shown below (only the portion of the input displacement for t>0 is shown).
Determine a) the Fourier series for the input (write down the first 3 non-zero terms below)
b) the steady state response of the system (write down the first 3 non-zero terms below).
c) about how many terms do you need in your steady state solution to have a good approximation?
Clearly show below what you need to put in your Maple worksheet and include a printout of your Maple worksheet.
y(t)
x(t)
k c
m
0.1 0.2 0.3 0.4 Time (s)
y (cm)
EM406 Examination II Problem 3 October 9, 2001
A second order system (m = 0.2 kg, k = 100 N/m, and c = 0.8 N-s/m) is subjected to the two situations shown below.
a) Initial conditions x(0) = 0.01, x( 0 )= 0. 3 m/s
b) Zero initial conditions plus the transient force shown below
where F 1 =20 N, b = 1 s.
Using Simulink determine the response of the system for the two cases shown above. Include a printout of your Simulink model, the forcing function, and the time response for 0 < t < 5 s.
Extra Credit Use Simulink to determine the time response when the system is subject to: zero initial conditions plus the transient force shown below (use the same F 1 and t 1 as in b)). Include a printout of your forcing function, and the time response for 0 < t < 5 s.
F (N)
Time (s)
F 1
t (^1)
Time (s)
F 1
t 1 2 3
1/2 a sin of magnitude F (^1) and period 2.
