Name:___SOLUTION
_______________________(Please Print)
Georgia Institute of Technology
Woodruff School of Mechanical Engineering
ME3015 System Dynamics and Control
First midterm: February 26, 2002
•
You need to show
all the work clearly.
Only answers or partial steps are not acceptable.
•
Transfer functions must be written in standard form: G(s) =N(s)/D(s) where N(s) and D(s) are
polynomials of “s” in descending order.
•
All problems are equally weighed.
Answer
three
of the four
problems.
•
Closed book/ closed notes, onepage formula sheet (with no examples) must be turned in with the test.
Check problem to be graded:
Problem 1:_____
Problem 2:_____
Problem 3:_____
Problem 4:_____.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document[1] (33.33%) Consider the following mechanical system, where
)
(
1
t
x
and
)
(
2
t
x
are the displacements
of the masses and
)
(
t
f
is an force external input.
(a) Derive the equations of motion for
)
(
1
t
x
and
)
(
2
t
x
.
(Common mistakes: sign error in the k
2
term)
See solution to text problem
)
(
2
1
1
1
1
1
1
1
1
x
x
k
x
k
x
b
f
x
m
−
−
−
−
=
±
±
±
)
(
2
1
2
1
2
2
2
x
x
k
x
b
x
m
−
+
−
=
±
±
±
⇒
2
2
1
2
1
1
1
1
1
)
(
x
k
f
x
k
k
x
b
x
m
+
=
+
+
+
±
±
±
(1)
⇒
1
2
2
2
2
2
2
2
x
k
x
k
x
b
x
m
=
+
+
±
±
±
(2)
(b) Obtain the transfer function
)
(
)
(
2
s
F
s
X
.
Note there are two unknowns,
)
(
1
t
x
and
)
(
2
t
x
.
Since we are
interested in
)
(
2
t
x
, we eliminate
)
(
1
t
x
by substituting it from Equation (2) into Equation (1).
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 UEDA
 Mechanical Engineering, Equations, Trigraph, SEPTA Regional Rail, dt, K1, D. E. Marsh

Click to edit the document details