Solutions (^191)
the time interval x can be obtained from the re-
lation
AP
Fm =—=mg.
By hypothesis, the mass M of the pan of the
balance is much larger than the mass m of the
ball. Therefore, slow vibratory motion of the bal-
ance pan will be superimposed by nearly periodic
impacts of the ball. The mean force exerted by the
ball on the pan is Fm = mg. Consequently, the
required displacement Ax of the equilibrium po-
sition of the balance is
Ax =
mg
k •
1.92. The force acting on the bead at a certain
point A in the direction tangential to the wire is
F = mg cos a, where a is the angle between the
tangent at point A and the ordinate axis (Fig. 186).
mg
Fig. 186
For the length of the region of the wire from the
origin to the bead to vary harmonically, the force
F acting at point A must be proportional to the
length /A. But F <mg, and /A increases indefinite-
ly. Consequently, there must be a point B at
which the proportionality condition is violated.
This means that oscillations with the amplitude
1 B cannot be harmonic.
1.93. It follows from the equations of motion for
the blocks
mai = Fel, 2ma^2 = —Feb
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