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PROBLEM 10.89
Rod
AB
is attached to a hinge at
A
and to two springs, each of constant
k
.
If
50 in.,
h
=
24 in.,
d
=
and
160 lb,
W
=
determine the range of
values of
k
for which the equilibrium of the rod is stable in the position
shown. Each spring can act in either tension or compression.
SOLUTION
Have
sin
cos
CB
xd
yh
θ
==
Potential Energy:
2
1
2
2
Vk
x
W
y
=+
22
sin
cos
kd
Wh
Then
2
2
sin cos
sin
dV
kd
Wh
d
θθ
=−
2
sin 2
sin
kd
Wh
and
2
2
2
2
cos2
cos
dV
kd
Wh
d
(1)
For equilibrium position
0
=
to be stable, we must have
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 Spring '08
 Jenkins
 Statics

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