Unformatted text preview: nic
(12)
with periods
l
h = √ ≈ 0.29l
(13)
23
m(k 1 k 2)
(a)
T2
1k 2
A quick second derivative test or ak plot of dT/dh veriﬁes that this is indeed a minimum, not a √ √ maximum. The minimum period is therefore
m
(b)
T2
k
k2
1 21 1 2
12 l + 12 l
= 2π
= 2π
Tmin = T
l
l
g 2√3
h= √
23 k1 l
√ ≈ 2.26 s
3g k2 4. A block of mass m is connected to two springs of force constants k1 and k2 as shown below. The
m
block moves on a frictionless table after it is displaced from equilibrium and released. Determine
the period of simple harmonic motion. (Hint: what is the total force on the block if it is displaced
by an amount x?
(a) ly to
M as
isk is
sk is
bly is
ition
f the
s k1 k2
m (b) Solution: Say we displace the block to the right by an amount x. Both springs will try to bring
Figure P15.71
the block back toward equilibrium  one will pull, one will push, but both will act in the same
direction. That means the net force is 72. A lobsterman’s buoy is a solid wooden cylinder of radius r
Fnet M It s w k2 h = − (k1 + 2 ) d so th
and mass = .−k1ix −eigx ted at onekenx = maat it flo...
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 Fall '08
 StanJones
 Physics, Force, Mass, Simple Harmonic Motion, Work, pivot point

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