(^192) Aptitude Tesi; Problems in Physics
where Fel is the elastic force of the spring, that
their accelerations at each instant of time are
connected through the relation a 2 = —a 1 /2. Hence
the blocks vibrate in antiphase in the inertial ref-
erence frame fixed to the centre of mass of the
blocks, and the relative displacements of the
blocks with respect to their equilibrium positions
are connected through the same relation as their
accelerations:
Axe=—
2 •
Then
Fel = —(^23 )k Ax^2 =3k Ax^2.
Consequently, the period of small longitudinal os-
cillations of the system is
2m
V 3k •
1.94. Let us mark the horizontal diameter AB =
2r of the log at the moment it passes through the
equilibrium position.
Let us now consider the log at the instant when
the ropes on which it is suspended are deflected
from the vertical by a small angle a (Fig. 187).
In the absence of slippage of the ropes, we can
easily find from geometrical considerations that
the diameter AB always remains horizontal in the
process of oscillations. Indeed, if EF 1 DK, FK =
2r tan a ;4–, 2ra. Rut BD FK/2 ra. Conse-
quently, LBOD a as was indicated above.
Since the diameter AB remains horizontal all
the time, the log performs translatory motion, i.e.
the velocities of all its points are the same at each
instant. Therefore, the motion of the log is syn-
chronous to the oscillation of a simple pendulum
of length I. Therefore, the period of small oscilla-
tions of the log is
T=21c1/
Ax1
T =2n
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