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h = √ ≈ 0.29l
m(k 1 k 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
1 21 1 2
12 l + 12 l
Tmin = T
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
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
s k1 k2
m (b) Solution: Say we displace the block to the right by an amount x. Both springs will try to bring
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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