3- 39
Problems and Solutions Section 3.6 (3.37 through 3.38)
3.37
A power line pole with a transformer is modeled by
mx
kx
y
˙˙
˙˙
+
= −
where
x
and
y
are as indicated in Figure 3.23.
Calculate the response of the relative
displacement (
x – y
) if the pole is subject to an earthquake base excitation of (assume the
initial conditions are zero)
˙˙
y t
A
t
t
t
t
t
t
( )
=
−
≤
≤
>
1
0
2
0
2
0
0
0
m
effective mass
k
effective stiffness
x
(
t
)
y
(
t
)
Solution:
Given:
y
kx
x
m
&
&
&
&
−
=
+
˙˙
˙
y
A
t
t
t
t
t
t
x
x
=
−
≤
≤
>
( )
=
( )
=
1
0
2
0
2
0
0
0
0
0
0
The response
x
(
t
) is given by Eq. (3.12) as
x t
F
h t
d
t
( )
=
( )
−
(
)
∫
0
τ
τ
τ
where
h t
m
t
n
n
−
(
)
=
−
(
)
τ
ω
ω
τ
1
sin
for an undamped system
For
,
2
0
0
t
t
≤
≤

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