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75. (a) The frequency for small amplitude oscillations is
fg
L
=
12
//
π
a
f
, where
L
is
the length of the pendulum. This gives
f
==
98
0
20
03
5
2
/(
./
)
/
(
.
)
..
π
af
ms
m
H
z
(b) The forces acting on the pendulum are the tension force
G
T
of the rod and the force of
gravity
mg
G
. Newton’s second law yields
G
G
G
Tm
gm
a
+=
, where
m
is the mass and
G
a
is the
acceleration of the pendulum. Let
G
G
G
aa a
e
=+
′
, where
G
a
e
is the acceleration of the elevator
and
G
′
a
is the acceleration of the pendulum relative to the elevator. Newton’s second law
can then be written
()
e
mg a
T
−+
=
G
GG
ma
′
G
. Relative to the elevator the motion is exactly
the same as it would be in an inertial frame where the acceleration due to gravity is
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 Spring '08
 Any
 Physics, Force

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