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150 Chapt. 16 Oscillations and Simple Harmonic Motion
are from the left and some are from the right. The block sits on a level frictionless Foor. The
springs are ideal. Each spring has a force constant
k
i
and equilibrium position
x
i
for the center
of the block: i.e.,
x
i
is where the block center would be in equilibrium if only spring
i
were
attached to the block.
a) What is the expression for the net force on the mass?
b) ±ind the appropriate singlespring equivalent
k
(i.e., force constant) and
x
eq
(i.e.,
equilibrium position) expressions such that the net force expression changes to
F
=
−
k
(
x
−
x
eq
)
.
Why is the
x
eq
the equilibrium position of the total system?
c) ±ind expression for the total system
ω
in terms of the individual spring
ω
i
’s and the total
system period
P
in terms of the individual spring periods
P
i
.
016 qfull 00370 3 5 0 tough thinking: twophase motion, collision and SHM
Extra keywords:
conservation of momentum, conservation of energy.
5. There is a hunk of mass 5 kg on a frictionless horizontal surface attached to a horizontal ideal
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 Fall '06
 Buchler
 Physics, Force, Friction, Simple Harmonic Motion

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