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107. (a) From Eq. 1612,
Tm
k
==
20
π
/.
4
5
s
.
(b) For a vertical spring, the distance between the unstretched length and the equilibrium
length (with a mass
m
attached) is
mg
/
k
, where in this problem
mg
= 10 N and
k
= 200
N/m (so that the distance is 0.05 m). During simple harmonic motion, the convention is to
establish
x
= 0 at the equilibrium length (the middle level for the oscillation) and to write
the total energy without any gravity term; i.e.,
EKU
=+
,
where
2
/2.
Uk
x
=
Thus, as the block passes through the unstretched position, the energy
is
Ek
=
005
225
1
2
2
.
( .
)
.
J. At its topmost and bottommost points of oscillation, the
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 Spring '08
 Any
 Physics, Mass

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