Exam
1
ME461,
June
4,
2014
Name
Ozze
LAJ-0r
t~i
a
z\
~ct
i2~1
i
~
(21)
I
2
Read
each
problem
carefully.
There
are
three
pages
and
three
problems,
each
worth
10
points.
Total
points:
30.
1.
(10
pts)
The
T-bar below
is
a
single
rigid
body
formed
by
two
rigidly
welded
uniform
bars,
with
each
bar
of
mass
in
and
one
of
length
L,
the
other
of
length
2L.
The
center
of
gravity
G
of
the
T-bar
is
thus
located
a
distance
3L14
from
the
pin
at
0.
It
is
attached
to
a
pin
and
hangs
as
shown,
with
a
spring
attached,
depicted
in
the
undeformed
state.
(Note
gravity
acts
downward,
and
must
be
accounted
for.)
Find
(a)
the
differential
equation
of
motion
for
small
angles
0,
and
(b)
the
undamped natural
frequency
of
the
bar.
Note
that
the
mass
moment
of
inertia
of
each
independent
bar
of
length
L
about
its
center
of
gravity
is
‘G
=
j~~mL2.
a
k
L
L
fri0
I~9
-
z~j
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4—I
\~~r
2
k(:fiL~9
4
—
—.
12.
4
IL
4±
2.
c
4..
v~
L
~-2frn)3
(z
w~L~
ö
~
(s~
(ox)
(~)
3.
2
2k-
L
4-
YML.
t~.
j
3
/
~
9
I
—
10
7~L
(ii~
