MEEN 364
Spring 2010
Problem 1
Consider the following electromechanical system. The coil generates a force that acts on
a steel core with mass m. The displacement of the steel core is x3 and is measured
from the cores equilibrium position.
L
F= kf if
iL
R
MEEN 364
Exam 2
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
Exam 2 April 18, 2007
7:00 9:00 PM
101 RICH and 114 RICH
Name:
Please circle your section below: Section (Lab Time):
501 (M 1:504:40 PM) 502 (
MEEN 364
Solutions to Exam 2
Fall 2004
Solutions to Exam 2
1) [15 points]
3s + 8
, u(t) = 3 sin(2t 2/3)
s + 3s + 12
The frequency of the output signal at steady state is equal to 2 rad/sec. At 2 rad/sec, the
magnitude of the system is
a) [6 pts] G ( s ) =
MEEN 364
Spring 2008
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
EXAM 2 April 16, 2008 7 PM 9 PM
Name:
Please circle your section below: Section (Lab Time):
501(M 1:504:40 PM)
504(W 1:504:40 PM)
502(T
MEEN 364
Spring 2008
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
EXAM 2 April 16, 2008 7 PM 9 PM
Name:
Please circle your section below: Section (Lab Time):
501(M 1:504:40 PM)
504(W 1:504:40 PM)
502(T
MEEN 364
Spring 2009
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
EXAM 2 April 15, 2009 7 PM 9 PM
Name:
Please circle your section below: Section (Lab Time):
501(M 1:504:40 PM)
504(W 1:504:40 PM)
502(T
MEEN 364
Spring 2009
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
EXAM 2 April 15, 2009 7 PM 9 PM
Name:
Please circle your section below: Section (Lab Time):
501(M 1:504:40 PM)
504(W 1:504:40 PM)
502(T
MEEN 364
Solutions to Exam 1
Solutions to Exam 1
Problem 1  Graded by Ram
Problem 2  Graded by Ram
Problem 3  Graded by Tolis
Problem 4  Graded by Vivek
1a) The Fourier transform of a function f(t) is given by
F ( ) =
f (t )e
j t
dt.
Therefore, subs
MEEN 364
Solutions to Exam 1
Fall 2004
Solutions to Exam 1
1) Consider the following continuoustime signal
xa (t ) = 3 cos(150 t ) 4 cos(800 t ) + sin(300 t ) + 2 sin(700 t ).
a) [10 points] What are the frequencies present in the signal x a (t ) and wha
MEEN 364
Fall 2006
Solutions to Final Exam
Sections 504506
1)
Kinematics Stage
The two degrees of freedom of the system are described by and respectively. The
position, velocity and acceleration of the CM of the pendulums are as shown below:
L
L
Ppendulu
MEEN 364
Fall 2005
Solutions to Exam 1
1a)
F (t ) = sin 2 (t ) + 3 cos 2 (t ) = 2 + cos(2t ).
F ( s) =
2
3s 2 + 8
s
.
+2
=
s ( s + 4) s ( s 2 + 4)
G (t ) = te t + 2t cos(t )
Use the following relations:
L[th(t )] =
d
H ( s)
ds
L e at h(t ) = H ( s + a )
MEEN 364
Spring 2006
Solutions to Exam 1
1a)
f(t) can be represented as
2t [U (t ) U (t 1)]; 0 t < 1
f (t ) =
2[U (t 1) U (t 2)]; t 1
Hence f(t) can be written as
f (t ) = 2t [U (t ) U (t 1)] + 2[U (t 1) U (t 2)],
f (t ) = [2 2t ]U (t 1) + 2tU (t ) 2U (
MEEN 364
Fall 2005
Solutions to Exam 2
1) For the electrical circuit, left loop:
R1i '+ vc = e(t )
(1.1)
where
dvc i ' i (t )
=
dt
C
R1
(1.2)
L
i(t)
i
Vc
e(t)
C
emf
Right Loop
Left Loop
R
For the right loop:
vc = L
di (t )
+ Ri (t ) + emf
dt
(1.3)
Where t
MEEN 364
Fall 2006
Solutions to Exam 2
1a)
Consider the electric circuit:
Writing the voltage balance equation for LOOP 1 and LOOP 2,
V (t ) + Ri1 (t ) + L
di (t )
=0
dt
But,
i1 (t ) = i (t ) I (t )
di (t ) 1
R
R
= V (t ) + I (t ) i (t )
dt
L
L
L
(1.1)
F
MEEN 364
Spring 2006
Solutions to Exam 2
1a)
Electrical Part
Writing the voltage balance equation for the electrical part of the DC motor, we have
V =L
di a
+ Ria + k e 1
dt
(1.1)
Free body diagram of the takeup capstan connected to the motor
T
1
Tm
J1,
MEEN 364
Solutions to Final Exam
Fall 2004
Solutions to Final Exam
1) [25 points]
(a)
&
Mechanical system: m& = b( y x) + k ( y x) + f c (t )
x
q
= e(t )
Electrical system: Ri +
C ( x)
(1)
q(t ) 2
&
and i = q
2A
q(t ) 2
& + bx + kx = by + ky +
&
&
mx
2A
q
MEEN 364
Fall 2005
Solutions to Final Exam
Sections 501503
1a)
From the shaded area, it can be concluded that
25 n 50
sin(32) sin(61)
1b) The transfer function of the system is:
3k
k1
1 +
Y ( s)
s s + 3k + 3
=
3k
k
U (s)
k
1 + 1 + 1
1
s s + 3k + 3 s
MEEN 364
Fall 2005
Solutions to Final Exam
Sections 504506
1a)
From the shaded area, it can be concluded that
25 n 50
sin(32) sin(61)
1b) The transfer function of the system is:
3k
k1
1 +
Y ( s)
s s + 3k + 3
=
3k
k
U (s)
k
1 + 1 + 1
1
s s + 3k + 3 s
MEEN 364
Fall 2006
Solutions to Final Exam
Sections 501503
1)
Kinematics stage
From the given figure, it can be seen that there are 2 rigid bodies. There are 2 degrees of
freedom and let the degrees of freedom be represented by the angular displacement o
MEEN 364
Solutions to Exam 2
Solutions to Exam 2
Problem 1 Graded by Vivek
Problem 2 Graded by Tolis
Problem 3 Graded by Ram
Problem 4 Graded by Ram
1)
Writing the voltage balance equation for the electric circuit, we have
Rm
Lm
+
im
Va

eb
dim
+ R m i m
MEEN 364
Solutions to Exam 2
Solution to Exam 2
1)
ia
Vin
e
For the electrical circuit part, we have,
di
Vin = Ra i a + La a + e
dt
&
e = K e m
(1)
(2)
For the mechanical part, the free body diagram is as following
r
T
m
J
B&m
k ( y r m )
&
&
b ( y r m )
MEEN 364
Solutions to Final Exam
Solutions to Final Exam
1)
The motor is characterized by the following two equations:
Te = K t i a (t ),
v = K &
e
e
Writing the voltage balance equation for the electric circuit, we have
La
Ra
+
va
ia(t)
ve
_
La
dia (t )
MEEN 364
Spring 2008
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
Final Exam May 5, 2008, 8:00 AM  10:00 AM
Name:
Please circle your section below: Section (Lab Time):
501(M 1:504:40 PM)
502(T 8:0010:5
MEEN 364
Spring 2008
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
Final Exam May 5, 2008, 8:0010:00
Name:
Please circle your section below: Section (Lab Time):
501(M 1:504:40 PM)
502(T 8:0010:50 AM)
50
MEEN 364
Spring 2009
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
Final Exam May 8, 2009, 12:302:30 pm
Name:
Please circle your section below: Section (Lab Time):
501(M 1:504:40 PM)
502(T 8:0010:50 AM)
MEEN 364
Spring 2009
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
Final Exam May 8, 2009, 12:302:30
Name:
Please circle your section below: Section (Lab Time):
504(W 1:504:40 PM)
505(R 11:102:00 PM)
50
MEEN 364
Exam 2
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
EXAM 2 JULY 25, 2002 @ 7 9 PM
Room 202T ENPH
Name:
Please circle your section below
Section (Lab Time):
301(MW 2:004:50 PM)
302(TR 2:004:50 P
MEEN 364
Solutions to Exam 2
Solutions to Exam 2
Problem 1 Graded by Tolis
Problem 2 Graded by Vivek
Problems 3,4,5 Ram
1)
The given electromechanical system is as shown
k
i1(t)
m
i2(t)
L
R
e(t)
b
F(t)
c
eb(t)
Core
LOOP 1
LOOP 2
Writing the voltage balan