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ME 375 – Spring 2011
Homework
No. 5
Due: Friday, February 15
Problem No. 1
(30%)
Recall the twodegreeoffreedom system in problem 3 of Homework No. 1 as shown below.
The differential equations of motion (EOMs) for the system in terms of the outputs
()
x t
,
t
θ
,
and input
ut
are:
(
2)
0
3
(
(
)
2
mx c x
R
k
x
R
mR
c R
x
k
R
x
ku t
θθ
+−
+
−
=
+
−
=
±
±±
±
±
±
(a)
Develop the transfer function
/ ()
Gs
Xs Us
=
corresponding to the output of
x t
and
input
.
(b)
What is the corresponding input/output differential equation with the output
x t
and
input
?
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View Full DocumentProblem No. 2
(40%)
A door closing mechanism, which is used to automatically close an open door, can be
represented as a simple secondorder system as follows:
JBKT
θθθ
+
+=
±±
±
where
J
is the door inertia about the hinges,
B
is the damping coefficient in the closing damper,
and
K
is the spring stiffness in the closing spring.
θ
is the angle of door opening, and
T
is the
applied torque when the door is pushed open.
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 Fall '10
 Meckle

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