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

CHAPTER 4
OSCILLATIONS
AND WAVES
4-1. Mechanical Oscillations
621. The vertical component of the tension force T is equal to F= t cos ex
(Fig. 477). For the conical pendulum F= mg, since the weight has no acceleration
in the vertical plane.
When the mathematical pendulum is deflected the maximum from the
position of equilibrium (through the angle a), the resulting force is directed
at a tangent to the trajectory of the weight.
Therefore, T = mg cos ct.
When the weight is deflected through the angle a, the tension of the thread
of the conical pendulum will be greater.
622. The period of oscillations of the pendulum on the surface of the Earth
is To= 2n .. / I and at an altitude of h above the Earth T I = 2n .. / I
JI g JI it
The number of oscillations a day is N1=24X60x60 ~l ~ :1. Therefore,
at an altitude of h above the Earth the clock will be slower by the time
To'
1it 1=N1 (T1-To)=k ( 1-T";)
The ratio between the periods is ;: =
as follows from the law of gravitation. Hence.
At kh ~ kh ~ 2 7 d
u 1= R+h - R - . secon s
V ~ = R:h
If the. clock is lowered into a mine. the acceleration
ti . g?, R-h. 4n RS 1 d
ra 101S--g=--r-. smce g="3 p R" an g2=
4n 1
= l' 3 (R - h)3P(R ~ h)t (see Problem 234).
Hence,
;:=V~=VRR h~1-2~
In this case the clock will .be slower by the time
Fig. 477
b-tl=k (
To ) kh.- d
l-r; =2R = 1.35 secon s