		    2   10

	    2   
      2 0 2   

     _2ਭ:.1 ⥬᪨  䨧᪨ ⭨, ᥪ-
		     1, .

     2 ࠡ:1 祭  ⥫   -
		  1 ⥬᪮   䨧᪮  ⭨;
		  1। ᪮७ ᢮ .

		   _I. ମ᪨ 

     ମ᪨ ﬨ  䨧᪮ 稭 20 뢠
    ६ 2t0  
_.1.0

			     7(0 27p       )
		    =  sin 7207 0t +7 f 20,
                             790 T7        0

 20 - 㤠 , 20 - ਮ .
	       27p
     稭  t +7 f 0   䠧,7 f 0- 砫쭮 䠧.
	       T
 10 mex10-1.pcx 130 45
䨪 ⠪  ।⠢  .1.
0

   1







			     .1.

       । ମ᪮  ᫥,  ਮ
  訬 ஬⪮ ६,  	祭
ண   筮 . ⢨⥫쭮,
1.0

               7(0 27p0       7)0         7{0  27p (  0  7 )     }
      =  sin 7207 0t +7 f 20 = A sin 720  720t + T720 + 7f0 720.
               790 T        700         7[0  T7  9     0     ]
0



                              - 2 -


      ६ 2t0 = 20 ᮢ蠥   .	㤠
 20 ࠢ ᨬ쭮 祭  2X0. 稭 7f0 ᮮ⢥-
  䠧  	砫  ६ (2t = 00)  뢠 -
砫쭮 䠧.
     稭		   27p
                            = 7w0                            (1)
			    T

뢠 㣮 (横᪮) ⮩.  ᫨ 砫쭠  䠧
ࠢ 7f 0= 7p0/2,  ࠢ ମ᪮  뢠
 :
			 =  cos(7w0t)  7  0		      (2)

 20 mex10-2.pcx 500 50
		     _II. ⥬᪨ ⭨

     ⥬᪨ ⭨  뢠  ⥫쭠 ⥬,
  ਠ쭮 窨,  ਪ९񭭮    쭮
,  令  ᮬ , ன  ன -
९   窥   室    ⢨
			         㣨    ⥫.	᫥-
   20			    ୮ ⠭	-
			         奬᪨   ࠦ   
			      .2.  ।⠢ ᮡ ⠫-
			        ਪ ࠤᮬ 2r0  䨫୮
			      :	⮭  ய饭 -
			      १  業 ਪ,    -
			      ९  ⮩.    2L
			        ॣ㫨஢  । 
			      ᪮쪨 ᠭ⨬஢    0.5  .
			      ਮ   ᮪ ( 105-3
	      .2.	      ) 筮     
			      ஭ ᥪ㭤.
      樨  ⭨ ᪫뢠   樨 -
ਪ   樨   ⭮⥫쭮  OO'. ७-
ॣ ⮬ 樨 ,  襬  樨 ⭨ -
⥫쭮  '  :

	       J4o0 = J4c0 + mL520 = 2/5 mr52 0+ mL520 .		  (3)


                              - 3 -

     ⭮襭 (3) ᫥  ⥮६  -⥩,  ᫨
,   樨 த  ࠤᮬ 2r0  ᮩ 2m
⭮⥫쭮 , 室饩 १  業, ࠢ

		       J4c0 = 2/5 mr52 0.

     ᬮਬ 砩,  	ࠤ	ਪ   ࠢ 
 :  2r0 << 2L0 .  (3)   ७	᫠
2/5 2mr520,   ࠢ  2mL520,  

			 J4o0 = mL520 .			      (4)

   ⮬ ਡ 2J0 ।, 祢,  让 -
᪮ 譮:
1.0

	     7D0J40	2   mr520    2  7(0 r 7)52
	       =   =5 0 720720 ,   7 0	      (5)
	       J	5   mL520    5  790 L7 0
0

  ᫮   業.  ⮬ (4) ਮ -
 ⭨    :
				4_____
			 = 27p0 7?0 L/g .			      (6)

       (6) ᫥, ਮ   ⥬᪮
⭨         2m0.  ⨬,   㫠 (6)
ࠢ    㣫.   筠 㫠  -
 ਮ  :
			4_________________________
		T = 27p ? 0L/g ( 1 + 1/4 sin520(7a/02)) . 	 (6')

      ⭨  ﭨ    業  殮  
窨 .	 殮 ୮ ⭨  ᮢ
筮  ᪨ 業஬ 殮 ਪ, ⮬ ।-
⢥ ७   ।⠢ .   ।-
 ᪮७ ᨫ 殮 ᬠਢ  ⭨ 
ࠧ  .
     ᫨ । ਮ   ⭨  ࠧ-
 ,  ᮣ᭮ 㫥 (6)  :
                    4______0                  4______
	   415 0= 27p ? 0L410/g ;	   427 0= 27p0 7? 0L420/g  .	      (7)


                              - 4 -

㤠 ।塞
                         47p520 (L410 - L420)
                   g =7 0 .                     (8)
			    T41520 - T4252

      ࠧ,  ⮣, ⮡ । ᪮७ ᨫ -
, 筮   ⥬᪮  ⭨    ᮮ-
騩 ਮ    .

			 _III. ७.

 ).    믮 ࠡ  ஢ ⠭:

     1. 	஭⥩   ᪨ 稪 -
⠭    ,      ,  ⮡
  ࠭	஭⥩ 뢠  誠    50
. 䨪஢ ᪨ 稪  ࠭ .
     稢 孨 ஭⥩,    稪 -
᪨ ⭨.
      ⮪    孥  ஭⥩ ⠭ ࠭
 ⥬᪮ ⭨.      ,  ⮡
    ਪ 뫠 த    -
᪮ 稪, ⮯ ⮬ 䨪஢ ࠭ .
     ਢ ⥬᪨  ⭨  ,  ⪫ ਪ
 4-55o0   ࠢ.
       <>.
     ᫥  ⥫ 2N0  (  N=107_020	)7  0
 <>.
     ६5 2t0    5 ࠧ   訡 -
७.    ⬥    ਪ 
誠 - 2n410.
     2.  ਪ  ᪮쪮 ,	㪮稢 ,  -
  ⮯ ⮬.   誠 ।	 
 ਪ - 2n420.  ਮ  ⭨ 2420.
     3.  㫥 9 । ਮ  ⥬᪮
⭨    2L41 0 2L420 .

			    4 0= t/N 			  (9)

     4. ᪮७ ᨫ 殮 ᫨   㫥  (8).  

                              - 5 -

訡 । 稭 2g0.  ⮢ 2n420 - 2n410  誠
 2L420 - 2L410.  室 ,   㣫 ⪫  ⭨
  묨.

     ). 믮  ࠡ   ⠭  㤮 -
᪨ 稪:

      1. ⠭ ࠭  ⭨.
      2. ⪫ ਪ   ࠢ  㣮 4-550.
 ਪ,  稢 ६ ᥪ㭤. ᫥ 
10 - 20 ,  몫 ᥪ㭤. ७ ६ -
 ந   5 ࠧ  ᫨ 訡. ᫨ 410.
      3.  ਪ  ᪮쪮 .,  㪮稢 . -
 .1-2. ᫨ 420.
      4. ᪮७ ᨫ 殮   㫥 (8).  ।
訡 ७.
 30 mex10-3.pcx 505 60
		     _IV. ᪨ ⭨.

     ᪨ ⭨ 뢠 ⥫,  ९񭭮  -
 ਧ⠫쭮 ,  室饩 १  業 殮,
 ᯮᮡ ᮢ  ⭮⥫쭮  ⮩    (.3).
,  ⭨,  ⪫   㣮 7a0    
                                ࠢ, 㤥  ᮢ -
   30                            ᪨    -
                                ਮ  ⠪ ⭨.
				   稬 १ 2J0  -
				樨 ⭨  ⭮⥫쭮  .
				 窠  C	 業஬
				殮.  殮 2F = mg0 -
				 ࠧ   ⠢騥,
				   - 2F420, ࠢ-
				 ॠ樥 .  -
				 㣮 ⠢饩  ⭨
				室  :

	      .3			  F410 = F770sin7a0.	 (10)

      ᭮ ண  ⮭    ⥫쭮 -
 (  = J7b0 ) :
                            J77b0 = - F41770L,                 (11)

                              - 6 -


 㣫 ᪮७ ࠢ:
1.0
                                 d527a
                            7b0 =  .                    (12)
                                 dt52
0

2L0 = C - ﭨ  窨   業 殮.   -
 ࠭ ⮬,    ᨫ 20 ६  ⭨ 
 ࠢ, .. 㬥 㣮7 a0.  .. 㣮 7a0 , 
sin7a ~0 7a0 
                           F417 ~0 mg7a0 .                    (13)

⠢ (12)  (13)  ࠢ (11) 稬,
1.0

		      d527a
                   J  + mgL7a0 = 0 .                   (14)
		      dt52
0

      襭  ᫥ ७樠쭮 ࠢ -
:
                         7a0 = 770cos(7w0t),       7 0            (15)

                              4_______
                         7w0 =7 ?0 mgL/J  ,                    (16)

2A0 - 㤠  ⭨.
      ७ (15), 稬:
1.0

     d527a0                 5      0 mgL   5 0        mgL
     = - A7w52770cos(7w0t) = - A  cos(7w0t) = 5 7a0 .    (17)
     dt520                        J               J
0

     ⠢ (15)    (17)  (14),   㡥,  
 ࠢ ⮦⢥ ࠢ .
     ࠢ (16)  (1), 稬:
				 4________
                         T = 27p ?0 J/(mgL)                   (18)

      ࠢ (18) ᫥, ਮ  㢥稢
 㢥祭  樨.

		      _V.  ⭨.

      砥 䨧᪮ ⭨    -

                              - 7 -

⭨. । ᪮७ ᢮    -
 ⭨ ᭮  ᢮⢥    窨    
業 砭:   ७ 窨   業 砭 ०-
 窠  ⠭  業஬ 砭.
      뫮 祭 ᮮ⭮襭:
                           4________
                   T = 27p ?0 J/(mgL) ,
 40 mex10-4.pcx 50 60
뢠饥 ਮ 20   䨧᪮ ⭨   
⮬ 樨 2J0 ⭮⥫쭮  砭 , ᮩ 2m0 ⭨,
ﭨ 2L0   砭  業   ᪮७ ᨫ -
				 2g0 (.4). .. ᮮ⭮襭
   40                            (18)   ᯮ짮  
				। 2 g0.  ⮣ -
				  20, 2J0  2L0  ࠧ
				१    2g0     
				(18).  뢠, ,  
				᮪  筮  
				⮫쪮 ਮ  20 ⭨-
				,  	稭 2J0  2L0 筮
				筮   㤠. -
				,   宦 ﭨ 2L
				  砭  業  -
				⭨	室 ।⥫쭮
	.4.			।  業 ,
				 ᤥ 筮 쭮 㤭.
     ⮨⢮ ⮤  ⭮ ⭨  । -
७ ᢮   ,  2 J0  2L0  	室	
   2 g0. ३  㦤 ⮣ ⮤.
     ᭮ ⥮६ -⥩,   樨 ⭨
⭮⥫쭮  砭 2 0:

		       J = J400 + mL520 ,			     (19)

 2J400  -  樨 ⭨ ⭮⥫쭮 ,  ࠫ쭮
 砭  室饩 १ 業   ⭨, 2L0 - -
ﭨ  窠2 0  2 02 0 .
     ⠢ (19)  (18), 砥:
201.0
			  7|\\\\\\\\\\\\
                         7/0 1  7(0 J407    )
		  = 27p0 7/0  720  + L720 .		     (20)
                       7?0   g  790 mL7    0
0


                              - 8 -

     㤨 ⢥  ࠪ  ᨬ ਮ 
 ﭨ   砭.   祭  2L0  ᨫ  -
  2M = - m772g772L770sin 7Q0 (.4.),  ६騩  ⭨ 
 ࠢ,  ⠭ 祭   ਮ	
१ ⠥.   । 2L 762 00  ᨫ 殮 ࠢ 
   : ⭨ 室   ࠢ-
.  ᮣ  㫮 (20):  7 2L0 760 07  0ਮ
701.07

			     1
		       T 7`0 7 6 $
			    7|\\
			   7?0 L
0

      ⭮ । 祭  2L0   ७  2J400  
ࠢ   2mL520  ᬠਢ 䨧᪨ ⭨  ⥬-
᪨    2L0.  ⮬ 砥 ਮ 
						   4_____
					    = 27p ?0 L/g.

 50 mex10-5.pcx 750 700
  50 				      ⠭ 2L0 ਮ
				     20 ᭠砫 뢠  -
				     ண  쭮  祭
                                     24m0 = 24min0,     ⥬  ᭮
				     ࠭祭 ⠥ 
				     2L0 760 7$0 :  (20).
					  ਮ  
						    4______
					      L4m0 =7 ?0 J4o0/m

				     ⢥  20(2L0) -
				       .5. 祭 2L0 = 0
				     ᮮ⢥ 業  -
	  .5.		     ⭨. ᫨ 訢 -
⭨   ஭  業 ,  ᨬ 20(2L0) 㤥
筮 ⠪ . ⮬ 䨪 20(2L0)   ᨬ ⢨,
ᮮ⢥騥    窨  ⭨ ᫥  ࠢ
  業 .    ஭   業    ⭨
     ਧ,   ਮ -
 ⭨ ᮢ.
       砥,   20 = 24min0 ⠪ 祪     業
, 祬 2L410 = 2L420 .
        ⠭    ⭨  ।⠢  ᮡ

                              - 9 -

⠫쭮 থ ,   ஬ 室   㧠 A 
B (.6).    ਧ  410  420   ६
  ভ  䨪஢ ⠬  ࠧ  窠.  ⭨
ᮢ蠥   ⨪쭮 ᪮. ६  -
 ,   ਮ  ⭨.
     ஡㥬  ⠪   2L410  2L420  ਧ 
ࠧ	஭  業 ,  ⮡ ਮ  ⭨
ᮢ:
			 (L410) = (L420).

        (20),  ⮣ 室 믮 ࠢ⢠
1.0

		    J4o0   4 0	 J4o
		   + L410 =  + L42
                   mL410          mL42

஥     2L410 = 2L420,  

			    J4o
		      L420 = 				 (21)
			    mL41

      ᫥ 砥 ਮ  ⭨

                         7|\\\\\\\\\\\\0        7|\\\\\\
                        7/0 1 7(0 J4o0     7)0       7/0 L410 + L42
T = T(L410) = T(L420) = 27p0 7/0 720 + L41720 = 27p0 7/0      (22)
                      7?0   g 790 mL410    700     7?4 0 7 0  g
0

     ⥫쭮, ᪮७ ᢮    -
  㫥
			47p52
                    g =  (L410 + L420) .                    (23)
			 T52
      	  (23),   宦  2g0  筮 
⮫쪮  稭:  ﭨ 2L400 = 2L410 + 2L420  ࠬ -
 ਧ  ਮ  ⭨ 2T0   2L410   "-
⮬"  2L420, ⠪, ⮡ 2T0 = 2T410 = 2T420.
1.0
		     4____
		    7/0 J
     稭 L4o0 = 7/0 뢠 ਢ  䨧᪮-
		  7?0   m
0
 ⭨ (.6).
 60 mex10-6.pcx 45 60
.
                             - 10 -


			6










			   .6

			 _VI. ७.

     1.  孨 ஭⥩  1805o0.
     䨪஢   ভ  ᨬ筮,  ..,  ⮡
   室   ভ,   㣮   
।.
      ਧ ⭨ ९    ஭  業
殮  祭  㪠 ᯮᮡ ⥬ ⠪ -
,  ⮡  뫨 饭    設.   
   ᢮  ভ,     
ﭨ  㧠.
     2. ⠭  ⭨      孥 ஭⥩ 
ਧ, 室饩   ভ.
      ஭⥩     ᪨ 稪 -
 ⠪ ࠧ, ⮡ থ ⭨ ᥪ -
 .
     ⪫ ⭨  4-55o0   ࠢ    -
.
      <>.
     ᫥  ⥫ 2N0  (  N=107_020	)7  0
 <>.
      㫥 (9) । ਮ  ⭮ ⭨  2T410.
     3.  ⭨  ९   ன ਧ.
      ஭⥩  ᪨ 稪  ६
⠪ ࠧ, ⮡ ⭨ ᥪ  .
     ⪫ ⭨  4-55o0   ࠢ, -

                             - 11 -

 .2  2T420  ࠢ  2T410; ᫨  2T420>2T410,   ਧ
६  ࠢ 㧠,  室饣     ভ,
᫨   2T420<2T410 -   ࠢ । ভ.
      㧮  ࢮ ਧ  !
     ୮  ਮ 2T420  ࠢ  稭 2T410.
       ன ਧ   祭 ࠢ-
 2T420 = 2T410  筮  0.5%.
     । ਢ  ⭮ ⭨ 2L400.
     4.  㫥 (23)  稭 2g0.
     5.  ॠ   㤠  筮 ஢ -
稭 2410  2420,   ਢ  譮 । 2g0.  ⮬
 ,   祭 ᫥ ⠢  
(23)?    410 7~0 420  譮  祭 ⢥,   
 ᫮   ᨫ쭮 .   -
㤭 㡥,  20    2410  2420,     祭.
⥫⢮ ᪠  ⢥ত  ।⠢塞  -
⥫. ⮡ । 稭 2L410  2L420 ਤ㬠 ⮩ ᯮ-
ᮡ, 騩  業 殮 ⭨.
     6. ⭮襭 2L410/2L420    ᫨誮 訬. 2L410 ᥣ
 2L400,  ⮣   2L410/2L420 稭 2L420 뢠 
 ਮ  १ ⠥.  ⮬ 㢥稢 ६
७   ஫ ᨫ ७,     뢮  
(18)  뢠. ⥫쭮, ⮡ 21.5 < L412/L422 < 3 0.
     7. 譮 । 2g0     (23):
401.0
		       ___________________
	       7D0g7     /( D0L 7)520 7  (0 7D0T7 )52
	       =7 / 20720 + 472072
	       g7    ?0  79 0 L7 0    9 0T7  0

0
		      _஫ .

     1.  ⮤ ७ ᪮७ ᨫ 殮  ⤠
।⥭? 祬?
     2.    筮 ⮢  ⥬, ᨫ
७, 㤠  ⭨?
     3. 뢥    (6')   ਮ  
⥬᪮ ⭨.
     4.  祣  稭 ᪮७ ᨫ 殮?
     5.     楫 ᯮ ⭨?
     6. ᬮ  ⭨,	騩  ⮭ -
த ভ  2L0   ᮬ묨	묨  ਧ.
  ⮬ 砥 㤥  稭 7D2g/g0   ਧ

                             - 12 -

⭮⥫쭮 業 殮 ⭨?    ᯮ  ਧ
   ࠧ㬭? 業 祭 20  7D20, ᮮ⢥-
騥 稭 7D2g/g0 = 5770105-20,   ⠪ ६, 室  -
 ᯥਬ   筮.
     7. 㫨 ⥮६ .
     8.  뢠 ਢ  䨧᪮ ⭨?
     9.   ᫮ 窠   業 砭  䨧-
  ⭨	ᯮ  ᨬ筮  ⭮⥫쭮  業
?
    10.   ﭨ  ୮ ਧ  業  -
ਮ  ⭨ ?
    11. ,  	窠   ⭨  窠  砭
  ࠧ ஭  業 .

	       _  譮 ७.

     - ᨬ쭮 ⢮ 塞  
        ⭨					       99
     -  塞 ६		       1-99999 
     - ࠡ 譮 ७ ६,	   0.02 %
     - 筮 ।  ⥬᪮
       ⭨  誠 ਡ,		     2 
     - 筮 । ﭨ  묨
       ਧ 䨧᪮ ⭨,		   0.3 

.
                             - 13 -


			   _.

     1. 쥢 ..  饩 䨧,.1.堭,  
, ୠ 䨧, "㪠", 1965.
     2. ५ .. 堭, "㪠",1965.
     3.  ., ᪨ ᭮ 堭, "㪠", 1971.
     4. 娭  ..  騩  䨧.,  .1,  堭.,  .,
1989.
     5.     䨧,   ।.  ..줨,
., 1983.









     ᠭ   ࠡ⠬    :
		     www.uniyar.ac.ru/~dingo
.
                             - 14 -




		᪨ ࠪ⨪  堭
		      ⮤᪨ 㪠







     ⠢⥫:         ⫠ ᮢ
		         ᠭ 
		           










	 ᫠᪨ 㤠⢥ 㭨. 1997
.
                             - 15 -













