Bukhovtsev-et-al-Problems-in-Elementary-Physics

OSCILLATIONS AND WAVES 129
city k and a pulley with a mass M. A string passed over the
pulley' connects the weight to the spring. Find the period of
oscillations of the weight if the pulley is a thin-walled cylinder.
633. With what frequency will a bottle with a mass of
m = 200 g and a cross-sectional area of A = 50 em- oscillate if
it floats on the surface of water in a vertical position?
Note. Remember that the period of oscillations of a weight
on a spring is T = 2n V; . where k is the coefficient of elasticity
of the spring.
634. Mercury is poured into communicating cylindrical vessels.
Find the oscillation period of the mercury if the crosssectional
area of each vessel is A = 0.3 ern! and the mass of the
mercury m = 484 g. The specific weight of mercury is
'V = 13.6 gfjcm s .
635. A mine pierces the Earth along one of its diameters. In
what time will a body thrown into the mine reach the centre
of the Earth? There is no resistance to motion.
636. A string secured at its ends is .stretched with a force f.
A point weight with a mass m is attached to the middle of the
string (Fig. 227). Determine
the period of small
oscillations of the weight.
The mass of the string
and the force of gravity
can be neglected.
637. How will the period
of vertical oscilla-
A
Fig. 225 Fig. 226
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