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Material Type: Exam; Class: Vibration Analysis; Subject: Engineering Mechanics; University: Rose-Hulman Institute of Technology; Term: Fall 2001;
Typology: Exams
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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.
Time (s)
t (^1)
Time (s)
t 1 2 3
1/2 a sin of magnitude F (^1) and period 2.