7 flffi: fflfffi ! " .". # .". .$. %ff & 'fifl . .$. (fl)ff "*)(fl . ( ff . ffi " fl . $. 'ffl+(fl ) " . "' ffi: fflfffi ! " (fl' " ( .". .$. fi# ff fi ( . ,! - ') (( ' ffi: # fflfffi ! " ffi " / : ( , ( ff " fl, , !. / # . ffi& " fl, . & fi !. ffl +"flfi fl. * fl ' "' * , . , !. ffl +"fl . # ff / , . , (fl !. , (fl. "fl ') ) 1 " " 2016 ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
) ,( 2 - ' )" # ................................................................................... 1 fi I ,( !(fl"1'ff !fl 1 ,( .................................................................. 10 2 fi)flfl ') 'flfl !(fl , ( ........................ 16 fi II * " / 3 * "' " ..................................................... 22 4 * "'& fl3 ....................................................... 29 5 * "' "............................................. 37 fi III / 6 / .......................................................................... 45 7 )ff & fl3!(fl ................................................... 53 8 ( ffl+!(fl ....................................................... 61 fi IV fl 9 fl ............................................................................ 69 10 )ff !(fl fl .................................................... 76 11 !(fl fl ........................................................... 83 fi V ', ffl + * 12 fl' ,ffl + ....................................................................... 92 13 fl' ,ffl + , / ' * ')% * # .......... 98 14 " 'fl',ffl + 2 * # ............................. 103 15 (' ,ffl + * ................................................. 108
fi VI * ffl+ 16 * ' ffl+ ............................................................ 114 17 fi)flfl * ' ffl+ ............................................. 121 18 "fl/(* ' ffl+ ................................................. 131 19 "fl/(* ' ffl+ RLC &# , 4" .................. 139 fi VII ' ,ffl + * 20 ' ,ffl + * ............................................................... 151 21 ' ,ffl + * fl ................................................ 159 fi VIII ' fl 22 ' fl ........................................................................... 164 23 )"" ') ' fl! " .......................................... 173 24 ') , fl,ffl ........................................................ 181 fi IX ( &( 25 ffifl fl!(fl fl" 1 ff ......................................................... 189 26 ( &(*ffi$,/ ') )fl ,( 5 .................................. 197 27 ) " & # .......................................................... 210 fi X ", + 28 fi # &) fl ................................................... 220 29 & ) ", + .......................................................... 233 30 2 # ') " (fl # &fi ) fl .................... 242 &"6 fl '& ສ fl ( .................................................................. 247 .ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
1 ' )" # 1. /fffi, !(fl" , " " )ff !(fl" 1 , ff , ! 2 , # fi"fi )ffl" flfi) flflfl , 'flfl ') )# fl 6( (& ", . )# ,(2 10 fi : , ( !(fl"1 '!fl, ff * " / , / , fl, ',ffl + * , * ffl+, ' ,ffl + * , ' fl, ( &( ') ", . + 2. /ff fl ,fi (fi , fl, ') !(fl% fl : 1) " - " " ,! 2/ " : !(fl"1 '!fl, ff * " / , / , fl') * , ' ,ffl + * , * ffl+, ' ,ffl + * , ' fl, ( &( ') ", . + - 2 # , ffl + , , ') & fl3 ,! 2 ' ,) ffi/ ') ffl , ! 2 "/ "# * . - 2 # " , " ') ! fi 1 *fi & ,(fl, &# )) & ') " "! (fl* . 2) - 2 " ffl " "& ,(fl. - !" " . - 2 2 # " ,! 2 fi ( ') fi ff fi "!(fl& ,(fl2ffl !. - 2 2 # , ffl + , , ') *) ffl ) & fl3 ffl + ( , ! 2 "/ "# . 3) / ) ') # - " ( ') ffl " fl. ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
2 - " , (4 & ,(fl ') % (6 fl ,ffl% . - )''%2 , " . - ,fflff !(fl" ') ,& ffiffi) &# fi , 1 ') fl . ff - % fl !(fl& ,(fl ') % (. 3. #,") "ffifl .5 .6 .7 "ffifl/( 2 2 3 "ffifl/ 2 34 68 2 34 68 3 34 102 4 ,ffl: - fl 34 ( , 2 1 "ffifl2ffl ( 55 4. ,( 2 ,(2 # ( ": 1) ,( !(fl"1'ff !fl , " *", " ,) fl; 'fl ffl+ ( 9 (Torque) ffifl( fl& fl, fi)flfl , , (, ffi fl , ( & ffifl , , " 2 ') ' "fl!(fl" 1 '!fl. ff 2) * " / * " / , , ( !(fl) * ", fi)flfl 2 * " ", * " (, * "" , ff * " fl , * " ( . 'fl * " " "" '& ') fl)" * " ". 3) / ffifi !(fl / , / fiff , ,fi !(fl, - , ) 4 , ( !(fl , (!(fl , ffl ,ffl!(fl , ( ffl + , )"" !(fl ') / fl ffl + fl.
3 4) fl ') * '!(fl fl, , ( !(fl fl ( ( ffl+, )"" , ( ') ffl !(fl fl). " ,! , ) fl, fi fl, * ff , ( fl)"!(fl fl, , / fl!(fl fl, ffi, + (Doppler effect), , ffiffl!(fl fl ') fi " fl. 5) ',ffl + * fl' ,ffl + , fl' ,ffl + , / ' * ')% * # fl & fl , & ',ffl + , 2 # ' ,ffl + * , " 'fl',ffl + 2 ' * , (' ,ffl + * ') * (,(fl. 6) * ffl+ ,# * ffl+, ) , ) fi , !(fl ' * ffl+, * ffl+2" fl/( '& , (fl& * , ' * ffl+2" fl/( '&, (fl (* , * ffl+2" fl/( '& # * # , * ffl+2" fl /(* , (fl& , , (fl ( ') & # # ') ') &# '!- , )# fl!(fl* ffl+, ffl + , " !(fl/ * ' ffl+ 1 , ') 3 , , ffl+ , " !(fl4# 'fl* ') * ' ffl+, * ' fl. 7) ' ,ffl + * ' ,ffl + * , "fl/( * " (LC), " ' ,ffl + * , fl ' ,ffl + * , )fl (, ,$ ffl + )fl )ff 'fl (IR), ' fl ffl" fl, ) fl () &$ "ffi(,) ffl + )fl ,- ("fl (UV), )fl ,( ') ) 5 fl ' . 8) ' fl / , ( ffl+, ) "!(fl' fl ffl" fl, ' fl! " ') ,/( (scattering of light), " fffl!(fl' fl ffl" fl, & ') ,fl,ffl . 9) ( &( fi ( ,) &$(, '/ )(fl( &(!(fl( # (Thomson), '/ # )(fl( &(!(fl$, ( (Rutherford), '/ )(fl( &(*ffi$,/& # ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
4 ( &(!(fl # (Bohr), (fi !(fl' fl ffl" ff fl, ) " -, !(fl ' fl ffl" fl ') ) " &( (Quantum Mechanics). 10) ",+ fi # &fi ) fl , fi ", , ) !(fl + # &fi ) fl , ( ffi ffi& (isotopes), 1)fi !(fl", , & + ) " , , fi) + flfl ", , ffiffl!(fl + # &fi ) fl , ( &) !(fl # &fi )fl ') (fl . 5. / - ( "/ ') ( / ff fl,fi (2ffl ) & , ff 4 !(fl . '&,1 fl6 fl2 & , # # # * " /* fl ff % . (" '& ) " '& & fl ') " *"- & fl . 4 " " fl * *", fl * . , / fl* " (ffl+ ffl+ , '&2 fi" , ,- 2 ' : (',( , 2/ fl ') (',( , 2/ fl. 2/ ff ffl+ ,*ffl ,& (/ : 1) ',( , 2/ fl ( (!# -1 () , ',( , 2/ fl (2ffl " "). 2) (',fi flfi ( * , ' "& ,(fl. 3) '/ " , ' fi . 4) fifl'&6 2ffl (fl , ffl 6 ( ffl (fl. 5) '// ,(# " , fl " . # 6) fifl'&2 ' , / ( 3 ( fl, ,& ffiffi) ,...). , ') (2,, , '"2? * 'fl fflfl' ? ') 'fl*2 fl2? )# ,) ", , ') ( (" &( ffi ,fi ! .7) ' ' 2 !" '2ffl " "
5 ( , 2/ fl) ffi, 2 & / &# fl3, : &fl 1 ,/ / # , ffl# +", )(fl ') " 2/ 2!(fl% . (',( , 2/ fl ' , %1 1(" 2ffl ' , - !(fl : " ,! # 2/ ') // ,(# !# 1 (2ffl , . (' , 2/ fl ',( , ,/ 2 fi ffl + fl " , , fl - , %(( ' ') (, fl / # ,4 )# . ') , " " ,fi ( fl!" 2ffl, ! . '%" 'fl ') ( , '" fl!(fl ') (" " ( ) '2ffl * / ffl " ') " fl" , &: fl, , ffl# +", )(fl, , ') ""!# & fl3 , : " ) , ( ,& ' ') (3 "fi , (2 3. % 1 (" ,(2" 1 (" ,(2" fl" % % 'ffl+fl ') ( % ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
6 2 (',( , 2/ fl, ", 2ffl * " ", & & "/ fl ') . / # , fifl'& “% 1 (” " , '& fl, “%( "" " /% # & ff ff (Facilitator)” 4 " " /,% "2ffl * fi "& ,(fl. " fl 2ffl " &))6 ') 6 fi fl24 3. ,fi(,2ffl - " & * % & (fl* & fl 1 # & ",(fl" 2 ! ( )# flffl fl? - WALT ') !( )# fl ( ffl ffl fl? - WILF. WALT What I am learning today 2 ! ( )# flffl fl? WALT '& ")( / *& # 6 ,fl !(fl'& )ffl (fl ,fi (2ffl !! # " ( / ff fl!(fl . WILF What I am looking for… !( )# fl ( ffl ffl fl? WILF'& ")( fi" , !( " / * '"2" * ) ,ff 4 !(flfi" ,! . ,fi(,2ffl - ( , " " ') fi 2 ("4 2 & fl3 , : '&& ffl # fl (Higher Order Thinking), (Communications)2ffl(fl ') '%" "/ (MindMaping),! " ,fi (2ffl ) & / ff ff fl!(fl ( 3. 6. - ( ') ,& ffiffi) ,fi& fl3 ( /&(fl* 2 # 2 (" ( ) : 1) & #fi & fi# 4 ,1fl ," , 1 -&(, ( , , " )"42 ff , , ) ff (fi ( 2ffl" .
7 2) !(fl/ fl (" 1ff/ & ) "1 ff/ & * ' : , (fl' %) ) * , , (fl' ' * , ,(fl' ( fflfi ff , * ' , (* , #6 fl, # $ & , '%' ", % ! , % *4, , (fl (* , ,(fl& * , * , 1 * ffl + 4# *, ,), # ' fl,...( ( fl6 ff fl %) */ fl, ,ffl + (2(fl1 . 3) flfi ', , -fl fi , " ) , ,( "! (fl& fl3. 4) ,fi& fl3 ,fi& fl3, ,fifi fl, fi ,(*ffl" (" ffi(), fi 1 , '& , ffi ,& , '%, & &) fl ') )"fl fl!(fl% (, fl 1 2'% fl, '% , fl" ') ff (3. 5) ,fi(fi ",& ffi$,/ ,& (LCD), / )(fl' ') ! # # fl(,& ' . 7. " ') , % 2 " ') , % 2ffl ,( 2/2 2 fl : 1) ,2!" - ( " ') , % , !&( # ') ! # * )# !" - (. / ff fl( & & #2 " ') , % ,fi ( "2ffl * %!(fl !. , 2 "ffifl ('& ) fl " ,# , % 3 2*) : " % ( (, " % 2! ( ') "% ffl +fl (. . "% ( ( ,fi (6fl, fl" !(fl & # / (2 " ffiflfl "" ffl+ -( 2. ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
8 !. "%2! (: fi ffl+fl ,)# & / 2- # fl, & (fl " (,fl" ,! 2/!(fl 2ffl (fl " ,! 2/&# ffl / ! # fifl2. . "%ffl+fl (: "% ffl +fl ( ' " % fi ffl +fl / 2- fl. " "% ( , ' 1 & # # ,(2 ffl + 1 # fi ') *2 # ; / ) /ff ff fl &fl*" ffl + -( 2, fi ( ,# fl"ff ( ') (!(fl 2ffl !, () ". 2) , fl ,( 2!(fl" 2ffl, ,1 fl" ,! 2/ " , (2" fi 1 " , " ') fi & ,fi # (2ffl ( (fl, fl ') . ",ffl / fl",( 2/ 2 fl : . " : " ,! 2/,(2fi1 fl" , " ffl+ !" fl " !(fl" "" 1 -&( ') " . !. " : - (( # ,ffl , ) fl %, , !# # , ffl ff +% ') ) fl ffi( fl( flffl + 1 ') " 6 fl ,/. - %fl & "/ fl, , ) fl , " / ,# (, fi , # !(fl ff ffl + )"4. - " 2 21 ffl-&( ') 2 # ' *!,! 2 " / "# # 2 fl . - " 2/2 " , , " ,! 2/2" # !(fl" . . & - " & # " " 2 ! # (* . fl , / fl& (fl2 fl, fi & # 'fl(( &"/ fl, : - " ffl "ffl ,! 2 " # , " ", fi & # ' *! ffl *2 fl" ') ( 3.
9 - " "2! & / # ff, " fi *ffl", " &fl2/, " ffl , " 1 & (fl ') ( 3. 8. fl'% (/ # ( ('& ) % (& (fl fl'% (/ # 2ffl)( ,fi ( & ffl + * 1 " ') ffl + ," ( #4ffl + . 9. ' '& # fl ( . '% ( ') ( 1) & (fl fl'% (/ # 2ffl )( ') 1 " ,fi () ff& /ff fl!(flffl + . 2) &(fl'& fl (/ # , # ,") 2ffl ( (fl / ff fl, , (2 ') / (2ffl # , fl& "6 fl'% (' UBD - 247). 3) / &# (fl ( (fl , (2, ,") ' ) , / # 2 /ff fl!(fl , fi ffl (fl, ,fl (*!( ( ff ffl + ( *2 (fl1 , , / # fl! / fi & "/ fl2 "/ "# ') , 2ffl , " 2/ "2ffl 6 ' *! ffl ,fi (ffl !# ffl ff +. 4) ,(2 ') # & (fl ( (fl ) " !(fl . !. ') 2 # (ff ( 5) ( (*" ff 2ffl 1 " & (. 6) " 2 (ff ( ') )(fl2 2ffl / # (fl' ". 7) ( ( ( ff 62 & " ') ffl * fl 2 (fl1 . , 2,") '& fl (& (fl # fl,1 fl" , 'ffl+ fl" ffl + !# ') (ff ( /2 '& )( ') " ffl + fl, 6 2 , 2%/, %%) ffl+ ffl * "" 2. ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
10 fi I ,( !(fl"1' ff !fl ,") 3 "ffifl 1 ,( 1. /ff fl 2ffl : - ') ,! 2/ffifi !(fl ,( , " *", " ,) fl 2 fl/) ff , 'fl ') ffi fl( fl& fl. - % !(fl , ( ') % , ( * . - *) " *" , " ,) fl ') 'fl !(fl , ( * - *) ffi fl( fl& fl!(fl"1 ff fl'& fl3* . 2. ,( 2&&# !(fl"1 ff 4 ,1fl 3/ ff !(fl" ff 1 ff)"'& , (,"fl ( ( ' ffi*)ffl fl/ ' ffl /ff fl " # 'fl. " *"!(fl , ( '( & !(fl " **2 - flffl"- ",") t ffl+ 2 T " ,)fl' ( & 'fl!(fl" *"2- flffl"- ",") t % , ( 2 0 1 = 2 t t 2 2 0 2 0 t 0 ( ) 2 t 'fl (Torque) '" 'fl fi ffl+ " 1 2fflff ((' ffl+ /ff *) & I
11 ffifl( fl& fl ' )ff 6 fl- fl, ! , (" 1 ff , fl, ) ( ,1fl" ( fl& fl2 !(fl"1 ff,fi ( fi !(fl ,( *". ffifl( fl& fl!(fl" 1 ff" '& & fl ! fl!(fl'& )" 1 ff & &) fl *) ffi fl( fl& fl!(fl" 1 2 ff fl& fl3/ "- # fl fl!(fl" 1ff ' ffifl( fl& fl ( I ) -" & " m ) 4 R ((' % / ff fl 2 2 5 I mR -" ffi fl" m ) 4 R ((' % / ff fl 2 2 3 I mR # & " m ) 4 R " L ((' !(fl # 1 2 2 I mR '% " m ) 4 R ((' % fl m &fl '% 1 2 2 I mR '% " m ) 4 R ((' % fl, fl - fifl '% 1 2 4 I mR 'fl" 1 ff( m " L ((' % / ff fl &fl ' fl" 1 ff 1 2 12 I mL # fl ffl+ "fl " m ) 4 R ((' # 2 I mR #- " m ) 4r ') R ((' # 1 2 2 ( ) 2 I mR r '% '/! fl!- " fl a "b ((/ ff fl 1 2 2 ( ) 12 I ma b R a b ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
12 3. ( ' . 7, * , * , * '% , ' fl* ') (3. 1 ,fl (*! " ,! ," * : https://en.wikipedia.org/wiki/Rotation_around_a_fixed_axis 4. / # ') ( fi # " , ,) (fl ,( ffi &fl 1 2ffl # " , : ,( ' , ( '"2?, /fl! % , (, % " *" , " ,) fl. fi "fi )ffl" fl % " *" ') " *" , fi "fi )ffl" fl( & ,) fl ') (& ,) fl '"2?. " , 2 !(fl",& , !(fl" ') " (fl& fl. ,fi ( fl" & # ,(fl2 "2ffl % ,! 2/ fl ! . ,( , " *" , " ,)fl ') %!(fl ,(: fi # ,! / # 24 ffi & fl 1 ! # , , ,fi ( fl" 2/, : 2 "/ "# , ,ffl 2' , ,( !(fl "1 ? ( ff !(fl&) , 2fi ) ...). !(fl"1 ff fl, ,ffl ) '"2? (' fl ') # fl ). / fi # & / , # , )(fl, fl, ') ( . / #: * ",/ - fl,fi (2 ' , 2 4 , /ff /,fi ff ( fl, & fl 1 # (& , : / fl fl, , ( !(fl /ff *4 *" (" *", *) fl, ) 6 '& )/ , ff '"2? (ffl fl?
13 )(fl ffl + 2ffl , )(fl ffi (* 2 ,/ *"') " ' "fl2ffl , ( , "fl , fl, " ') "&( 1 # ') ( . ( ,fi ,&" /ff 6ff , fl /, ( "" *" , , " ,)fl, ') " **, , '& ( & ,)fl , " *" ') *) fl,6 '& )/ ' ff " '& & fl ! *) ffl fl)ffl" fl/ ff , fl, ffl ' 4 " " 1 / ff flffl fl/ ' ffl+ , 2" *" ') *) fl, !(fl ffl# + !. / ,- # fi"fi !(fl % , ( . SRv RaR ; ; ,fi(2ffl ,! 2/ % , ( % , ( fl& ) fl. % , ( % , ( 0 v v at 0 t 0 ( ) 2 v vt s 0 ( ) 2 t 2 0 1 2 s at v t 2 0 1 = 2 t t 2 2 0 v v as 2 2 2 0 2 'fl ') ffi fl( fl& fl: , 2 !(fl",& : F ma % , ( I ') fi"fi )ffl" fl'fl " 'fl F R 2ffi fl( fl& fl I " m !(fl ,( ') " ,)fl " ,) fl a !(fl ,( . s v 1 2 3 ,- " *" , " ,)flfi ( fl! % *) : t ') t ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
14 ,- " *) ffi fl( fl& fl!(fl" 1 ff fl& fl3, ' ,) & "6 fl 2' ,fi (2ffl " ,! 2/ ') ,B 2 *) ffl +fl/ fi # ffl ff +,(2 * fl4 ( , (- fl ') 2ffl" . 5. " ') ,% - , ( : % &( 1 " # !(fl ,fi (&) )" ,! 2/, " !(fl ,fi ( "*ffl 24 ffl + ffl"! # 24 . - ,2)ffl" fl ,# / ') (: # fl, " ,( 2/2 , " 2/2 1 !(fl% ,fi ,&, ') # ,ffl , fi )" , ffl ff + fl)" ') ( ffl , ff ffl+ ff . - ,ffl +fl: fl, ffl ff + !(fl " 1 & " fl / ff fl*" # ') % &( ') ' " . ( ( / " ffl+fl ') ( 3 & (4 . &( #1 ') ' ,B ffl 1. fl : 100 rad/s ; t 20s *) : ?; ? 2 # 100 2 5rad/s t 20 2 # 0 ( ) 2 t t "1 ,)ff ,( / fi "fi 0 0 /* 100 20 1000 rad 2 2 t 2. 2 # I ') Fr &( 2 I 10kgm 3. fl : 2 m r 8kg; 3dar/s ; 0,25m *) : ? 2 # 2 I mr 2 8(0,25) 3 1,5 Nm
15 4. fl : m r 5kg; 0, 2 m; = -1,1Nm 0 = 210 (/ 210 2 210 2 3,14 22rad/s 60 60 0 t *) : t ? 2 # 0 ( ) t I I t 2 2 0 0 ()() 5(0,2) (0 22) 4s 1,1 t t I mr t 5. fl : 2 r t 0,5m; 2rad/s ; 20s *) : S ? , 2 a r 0,5 2 1m/s 2 # 2 0 1 2 S at v t '& 0 v 0 /* 2 1 1 1 20 2 200 m 2 2 S at 6. 2 # I &( 1Nm 7. 2 # : I ') t &( 2,5rad/s ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
16 2 fi)flfl ') 'flfl !(fl ,( ,") 3 "ffifl 1. /ff fl 2ffl : - ') ,! 2/fi)flfl , , (!(fl , ( ((' fl ') ' ((' # fl , ) , , (& ') 'flfl !(fl ,( . - fi) flfl , , ( ') 'flfl !(fl , ( ') ,( . - 2 # , fi) flfl ,! 2 ' ,) !(fl , ( . - ( " , ( fi2 "/ "# * . 2. ,( 2&&# . fi)flfl ,,( 1) 2 !(fl"1 (ff (' fl , !(fl2fi) , 4 , ff fl , &. *) fi) flfl , , (2 1 2 2 E I k 2) 2 !(fl"1 (ff (' # fl , : !(fl fl) ( (' , fl' ,# ( *,)(3 ffl+ ," ( 6 fl- fl" , ( ' flfi) fl fl ,, ( ' % " !(flfi) flfl , , (!(fl ') fi)flfl ,, (!(fl , ( !* 1 1 2 2 2 2 E I mv k !. ffi,& # ffl+ ) ,,(& ffi,& # ffl + ) ,, (& ' ) ," ,& 'fl,1fl , fl , % )ffl" flffi fl( fl& fl " *" L I ffl+ ," ,&) ,, ( ," ,&& '-# fl L PR mvR
17 (& 'flffi,& # & ,") , 'fl 2 ,fi (2ffl, L t ffl+ L t . 'flfl !(fl 'flfl !(fl '% )ffl" fl'fl 2 " 1 ff "1 ff " ** dW d . 2 # !(fl' 'flfl fl4 / *) & : W . ( / 'flfl !(fl fl, 'flfi)flfl !(fl . W E k ffl+ 2 2 0 1 1 2 2 I I fl , 2 , ( fl'' fl ') # fl ,# *& , fi) flfl . 4 " " 1 1 2 2 const 2 2 E I mv k )# fl!(fl , ( *) & : . . dW d P dt dt fl. ' "fl!(fl" 1ff ' "fl , ,( * 2, fl,,( " : , ( (", ' "fl' # *fi / ) ,1fl'fl& ( ,( " : , ( " (Simple Harmonic Motion, SHM) , fl % !(fl , ( : ( ) sin( ) t xA t ,( " 4 ) # : 1) ,( !(fl"1 ff& ) # # (Spring) 2) ) * "" ( Simple Pendulum) 3) ) * " ( Torsion Pendulum) 4) ) * " ( Physical Pendulum) , fl/* ,- 2fi * "& # * 3. ( ' .7, fl) # (, , , - " ,ffl + , )# # , * . ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
18 4. / # ') ( "" fl" "! (fl, : (fl (& fl3!(fl , ( ffl fl' ? ( ,, ,,, ,,, I RvaS ) /fl! % fi "fi " *", " ,) fl, *) fl,, " *" , " ,)fl ') 'fl !(fl . ( ;;; ; ; d d v R a RS Rd I dt dt ) "fi) flfl , , (!(fl , ( , , fi) flfl , ) ,, (. / fi # ,! ffl "! # 24 ffi2ffl , ( ') ,( ffi( fl2 fi) flfl , , (!(fl , ( . " m 2 ,( ) " ffi fl( fl& fl I !(fl ,( , " *"2 ,( ) " *" !(fl , ( . fl , ! * . fi)flfl , , (2 , ( : 1 2 2 E mv k fi)flfl 2 , ( : 1 2 2 E I k & fl 1 " # 2 , ( , fi) flfl fl (flfi ( * # ? ')" fi # , )(fl ( fl fl) # *& fi) 2ffl fl, ') "& fl # 1 ( " fl, ,ffl , ( / '? '2' ? / ( ,fi " !(fl"1 ffi ff ' ,( * , fi) # flfl !(fl , ( /flfi) flfl !(fl ') fi)flfl !(fl , ( , fi) fl fl)"6 '&)/ !(fl , ff ( # # 'fl. / fi ' ,) & "6 fl& ' ffl+ 4 2 ,) 24 ,fi ( fi # ,B ' & " ,4 . . ffi,& # ffl+ ) ,,(& 2ffl"! # (ffi # ) ,, (!(fl , ( fifl'& 'fl ) ') ffl "- "2 *) .
19 1 P ') ,, ( ') L ') ,, (& ') " m 2 ,( # ) ffi fl( fl& fl I 2 ,( ') " *"!(fl ,( v # ) " *" !(fl ,( ,( P mv /* L I ') 'fl 2 , ( & 'fl) ,, (& d L dt / fi ' ,) &"6 fl. !. 'flfl !(fl : / : , # (fl& 2ffl &fl !(fl"1 2- ff fl (, , # ...) ')"1 " , (, 2 " 'fl,fi ( "1 ff% , ! ' ffl fl? fi" , *%) fl (( # ? , 2? (W FS ) / 2ffl * ( (' *2- fl')"( " 2 , ( , # " , 'fl 2 ,fi (2ffl" 1 ff''fl ') *) fl**& " fl ' " **. , 'flfl !(fl ,# % )ffl" fl'fl " **W . . / fi # ' ,) & "6 fl fi # ffl ff + * fl4 ') ( " . 5. " ') , % 1) , ( (: % &( 1 2,") " # , " ,! 2/" , "! (fl 24 ffl + -( 2 # 2) ,2)ffl" fl # / (: # fl, " ,( 2/2 , " 2/ # 1 ,fi ,&, ') # ,ffl , fi ) " , ffl ff + fl)" ') ( ffl fl, ff ') ff . 3) ,ffl +fl: fl, ffl ff + !(fl " 1 & " fl/ff fl*" # ') % &( ') ' " " ,! 2/ffl+ # ( ( / " ( ffl + fl, / " ( ( /24 & # *. ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
20 &( #1 ') ' ,B ffl 1. &( . 2 5(3) 22,5 J 2 Ek 2 1 2 2 Ek mv !. 33,75 J Ek 2 , fi) flfl , , (: 2. &( . v 4, 47 m/s 2 , fi) flfl , , ( !. v 3,65m/s 3. &( v 5,16 m/s 2 # , fi) flfl 4. fl : 1 2 2 5kg 1kg =0, 2 m = 2 m =10 m/s m m R h g ,( &fl/ ,) ff & (1) ') /ff "1 ,ff ( **(2) &fl,) &/ )"fl fl 2 m. , /,) ff &/ fifl'& fi) flfl & fl ') fi) flfl , ,(!(fl !(fl4 )( C E m gh 1 1 ,(" 1 ,)ff ,( # flfi) flfl , ,(!(fl" 1 ff A 2 2 2 1 1 1 2 2 E mv I , fl 2 2 1 2 I m R ') v R / , fi) flfl , 1 2 2 22 11 2 2 1 12 2 1 1 2 1 11( )( ) 2 22 1 1 ( ) 2 2 2 2.5.10.2 400 1 1 11 5 2 2 20 m/s 11 E E v m gh m v m R R m gh v m m m gh v m m v v h 1 2
21 5. &( 240J Ek 2 fi)flfl 1 1 2 2 2 2 Ek I mv 6. &( 500J Ek 2 fi)flfl 1 1 2 2 2 2 Ek I mv 7. '% - fl" m ') ) 4 r 1 '% fl " fl& fi ' # &) ') ' / ff fl!(fl'% !- fi .1 " fi) flfl ,, (!(fl ffl+ " fi) fl, , (!(fl , ( / , ? ' : fl : " m ') ) 4 r ffifl( fl& fl!(fl'% ' % / 2/ fl ff 1 2 2 I mr *) : 1 2 ? k k E E ffi # 2ffl 2 1 1 2 Ek mv 'fi) flfl , , (!(fl , ( 2 2 1 2 Ek I 'fi) flfl , , (!(fl 2 22 2 2 1 11 1 ( )( ) 2 22 4 k v E I mr mv r 2 1 2 2 1 1 2 1 2 4 k k mv E E mv 8. &( 2 L mvr 4kgm /s ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
22 fi II * " / 3 * " ,") 3 "ffifl 1. /ff fl 2ffl , , ,! 2/ ') // #*: - !(fl * "' ". - *),( , *) , " 1, ,") (", , ') , # (!(fl * ". 2ffl : - ( ') fl* % !(fl * "' ", : % *) ,( , " *", " ,) fl, " 'fl, fi)flfl !(fl * ". - fl* fi "fi )ffl" fl" *" , " 1 ') ,") (". - 2 # % * "' "' ,B ffl "! (fl* . 2. ,( 2&&# - * "' " ' , ( !(fl"1 ' ff * % &fl ff fl!(fl) ffl + ' , ( # '& # ,(fl , : * "!(fl) & ff !(flffifl () * " ") ') * "!(fl" 1 ff 1 % 2 ) # # , &. - % * "' " 2 2 2 0 d x x dt - % *), ( !(fl * " 0 x A sin( t ) ffl+ 0 xt A t ( ) cos( ) x '*), ( !(fl" 1 ff ,( ** (2 &fl ff fl!(fl )) , fl ffl"- ", ' (m), (t + 0 ) ,(" : , (Phase Angle) ffl+ , (Phase) ffl"- ", rad; A '*), ( 2ffl !(fl" ff 1 ff * " ffl+ ,(" : * ) !(fl * " (Amplitude) , fl ffl"- ", ' (m)
23 4 " " xmax = A; '" *" , ( !(fl"1 & , ff , ffl"- ", rad/s. - fi "fi )ffl" fl" *" , " 1 ') ,") (" 2f '&" T f 1 , fl T 2 T ', ") (" , fl' ,") "1 ,ff ( * "** - fl( ') ffl"- ", " (s); f '" 1 !(fl * " ffl"- ", ' (Hz) ffl+ , (&# " (( / s). - % " *"!(fl * " " *"!(fl"1 ff * "' % & ) ! # - fl!(fl*),( 'fl & ,") . 0 v xt A t '( ) cos( ) 22 xAv ,(fl4 'fl2ffl,ffl " " *"!(fl" 1 ff * "6 '& )/ ff 2 " (+) 1 " 1 ffl , ff ( ,! ffl /ff &fl ff fl ') , ) (-) 1 " "1 ,ff ( (( / &fl ff fl. - % " ,) fl!(fl * " " ,)fl!(fl * " ' % & ) ! # - fl!(fl" *" & ,") ffl+ ," *" ' % & ) ! # (fl!(fl*), ( & ,") ,(fl. 2 0 a vt A t '( ) sin( ) xa 2 2 * "' ", " ,) fl, (& "fi "fi fl *), ( . ,(fl4 ) ( -) 'fl2ffl, " ,") 2fi" # fl fl ! . ffi ,fi ," ,&" ,) fl,") 2 # ,! ffl /ff &fl ff fl. - % fi) flfl !(fl * " fi)flfl / !(fl * "' % " fi) flfl , , ( ') fi)flfl & fl!(fl" 1 ff,(fl. EE E k P ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
24 + fi)flfl ,,( 2 2 1 E mv ,(" *"!(fl" 1 'ff 0 vAt sin( ) 22 2 2 2 0 0 1 1 sin ( ) sin ( ) 2 2 E m A t kA t k + fi)flfl &fl 2 2 1 E kx P 1 ) # # 6 (( *) 0 xA t cos( ) 2 2 22 2 0 0 1 1 cos ( ) cos ( ) 2 2 E kA t m A t P , fl 2 k m '" '!fl!(fl) # # ffl+ ,(" : # !(fl) # # ffl" -"" ' , N/m; x '*)6 ffl+ ffl!(fl) # # . fi)flfl / : EE E k P 1 2 2 2 m A 1 2 const 2 kA fi)flfl / !(fl * " # 'fl& ,") . 3. ( flfi : ' 7, " ') (3 "! (fl. , (ff (: )# # ; (" 1 -ff !- 10g, 20g, 5og, 100g; , ) )fl!- ( ') * ' " ' . '% ,/ ! "( ffl + '& 3.1, 3.2 ') 3.3. 1 ,fl (*! " ,! ," * : https://en.wikipedia.org/wiki/Oscillation 4. / # ') ( / # 1: , (# !(fl , ( ' * ". fl , " " " , ( '& fl3 * , : ,( , , ( ffifl ') , ( , &. ffl +fl/ /fl ,!# " , ( ' * " '# , ( ) , (" , ( , / ffl + 2ffl , )(fl ffi,( , ( ( " m ')", 2ffl * "* ffl + ,( )# # " m 2 ') " fl2ffl 6 (( ')"" fl2ffl " 1 ,ff ( * . 2ffl 2 ffifl/ ,") , ( !(fl
25 "1 ' ff * ,fi ("' ,") ("*fi (3 . / ,( 3.1 'fl2ffl , fl') " ffl ff + !(fl * " ') fl % * " " . / # 2: ( ,ffl% !(fl % *), ( ') ) & fl32 % fi (ffl "- ", / " fl % " *" ') " ,)fl!(fl * " ffi( fl2 " *", " ,) fl,* ')"'& , 'fl!(fl*),( , " *" ') " ,) fl fl2 3.2, 2ffl , flfi ( ( )ff !(fl, 'fl'&)( . / # 3: ') " , ,B ffl& "6 fl, ( /,( & ' ffl+ ,(# ,B ffl( ,B ffl& "6 fl *# . / # 4: fi # fl % fi) flfl !(fl * "' " ffi 2 # !(flfi) flfl * ') , 'fl!(flfi)flfl , ,( ') fi) flfl & fl fl2 3.3 ')"fi ( ( " 4 !(fl , 'fl. / # 5: ffl ff +,(2 # fl4 * ( , (- fl ,fi (2ffl * # /ff fl ') 4 !(fl . 5. " ') , % 2ffl &( 1 ! # # 1 ') ' ,B ffl! # 2. fi / ) / : - " 2/ ') 1 !(fl # . - " ,ffl !(fl . - ( 4 !(fl 2 & / . # - " "2'& ) / !(fl # '& ) . - " 1 & (fl!(fl # ,ffl ') ' ,) & "6 fl ') ,B ffl 2ffl. ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
26 ,B ffl 2ffl ' ,B ffl ! # 3 ffl !# 11. &( #1 ') ' ,B ffl !# 1 ') !# 2 2ffl, fl2 '. 3. ! % * " & ,") / % * "' " 0 xt A t sin( ) 2 A 3cm; rad/s T ') " 2,") 000 t x 000 xt t 3sin cm " *"!(fl," 1 ff * "2,") t = 2s. / vt x t t ' 3 cos 6, 28 cm/s 4. . " *"!(fl * " / 2 314rad/s f !. % *), ( 2'& )/ ,") ff / % * "' " 0 xt A t sin( ) xt t sin100 m . " *"!(fl," 1 ff * "2'& )/ ,") ff vt x t t t ' 100 cos100 m/s 314cos100 m/s fl. " ,)fl!(fl," 1 ff * "2'& )/ ,") ff 2 2 2 2 at v t x t t t ' '' 100 sin100 m/s 314 sin100 m/s /. *),( !(fl, " 1 ff * "2/ ,") ff 0,01s, / % * "' " xt t sin100 m x t sin100 0,01 0 "1 %ff &fl ff fl. . " *"2ffl !(fl, ff " 1 ff * ": v A max 100 m/s . fi)flfl fl4 !(fl, " 1 2'& ff )/ ,") ff 1 1 2 22 3 4,93 10 J 2 2 E kA m A
27 5. . fl % * "!(fl" 1 ff ( . / % * "' " 0 xt A t sin( ) * 40rad/s k m ') " 2,") 0 0 t x 0 8cm , fl 0 00 0 xA t fl sin( ) 8 8sin 0 0 0 sin 1 rad 2 % * "' " 8sin(40 ) cm 2 xt t !. fi)flfl )"!(fl) , 1 2 23,04J 2 E kA . /ff "1 fffi) flfl , , ( ') fi) flfl & fl, ' : 1 1 2 2 2 2 2 22 2 2 E E mv kx m A x m x k p fl 5,66cm/s 2 A x fl. " *"!(fl"1 2! ff # : 2 2 v Ax 160 2cm/s /. "1 ,ff ( 1 (2 ,") , : 2 s 0,157s 20 T 6. &(: ! # # fl 1 & (fl % * "' " 0 xt A t sin( ) A f 10cm; 2 100 rad/s ') " 2,") 0 0 t x 0 5cm , fl 0 00 0 xA t fl sin( ) 5 10sin 0 0 0 1 sin rad 2 6 % * "' " 10sin(100 ) cm 6 x t t ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
28 0 ffi 45 ffi 30 A B T mg cosffi mg h cos 45 cos30 7. #&(: !# 1 &( fl 2 # " 'fl!(fl * "' " 2 F t ma t m x t () () () 2 rad/s T 2 ; 1 0 0 ( ) sin( ); 0 ( ) 10 sin 2 t xt A t xt 2 ( ) sin N 4000 2 t F t 8. #&(: !# 1 &( fl / " *"!(fl * " 2 2 v Ax *: 2 22 2 2 22 2 1 1 2 22 2 2 22 2 2 2 3 2,4 ...............(1) 2 2,8 ...............(2) v Ax A v Ax A ,( % (1) ffl % (2) *: A 3,1cm 9. #&(: !# ! 1 &( fl 2 # , 2 !(fl",& 2 cos30 B c v fl F ma T mg m 2 cos30 B v T mg m *) " *" / ff B B v / , fi) flfl / E E A B 1 2 2 2 2 cos30 cos 45 2 mgh mv v gh g B B T 5,9N 10. #&(: !# ! 1 &( fl / " *"!(fl * " 2 22 2 v v Ax x A ffl ff fi ! " ' x 6cm 11. #&(: !# 1 &( fl / % * " " 0 2 x A t A tA t sin( ) sin sin T / ffi/ 1 1 sin sin s 2 26 A x At t t
29 4 * "'& fl3 ,") 3 "ffifl 1. /ff fl 2ffl , , ,! 2/ ') // *# : - * " "'& fl3, : * "!(fl) * ") # # , ) * " ", ) * " , ) * " , * " ( (, * "" ff ') * "' fl . - *) " *" , " 1 ') ,") ("!(fl * " " '& fl3. 2ffl : - ( ') fl* % !(fl * "' ",fi& fl3. - fl* fi"fi )ffl" fl" *" , " 1 ') ,") (". - 2 # " *", " 1 ') ,") ("!(fl * "' & fl3 ,fi (*) ,B ffl "! (fl* . 2. ,(2& & # 1) * "!(fl) * ") # # &fl ff fl!(fl) ' &fl&( " 'fl fl)" 2 " 1 ff fl4 , . " 'flfl ' " 'flffl 6 !(fl)# #F kx . fl , " *", " 1 ') ,") ("!(fl) * ") # # /* m k ; m k f 2 1 ') k m T 2 - 1 & # )# #ffl+ () , # ffl 6 fl)"!(fl) ) # # . 21 111 kkkr - 1 & # )# #ffl+ (!- , # ffl 6 fl)"!(fl) ) # # . 21 kkkr ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
30 2) * "!(fl) * " " " *", " 1 ') ,") (" * "!(fl) * " " g ; 1 2 g f ; T 2 g ,( g , " ,)fl1"fl- , fl ffl"- ", m/s2 , 2 ) # ) * " )# fl, ( " ,) fl a ') * "* , (3% &fl ff fl. ,") ("!(fl * "* / % T 2 g a g a '!- !(fl," ,&" ,) fl fl)" fi 2ffl) , ( * ". 3) * "!(fl) * " "1 ff * "(( (ffl (!(fl * 6 fl, ) ,(" : ) * ". 1 " ! - !(fl"1 ff fl " (ffl + ,(" : ' ) * " ", 1 " " 1 ff !- 2ffl &(fl ,( " : ) * " . &fl ff fl!(fl) ' &( /1ff "fl- ( fl" ) C !(fl"1 " ff m (6& , &fl % (ffl ( O. 2 &fl ffi fl!(fl" 'fl1 "fl- P , . 2ffl OI 'ffi fl( fl& fl!(fl" 1 2 ff / '!" ff O. " *" , " 1 ') ,") (" * "!(fl) * " fl : OI mgd ; OI mgd f 2 1 ') mgd I T O 2 1 " fl * "ffl 6 / " ff / ff " !(fl" 1 ff * "2 / '!" ff O ffifl( fl& fl!(fl"1 /, ff 2 I md O . 4) * "!(fl) * " ) * " ' ) * "- fl!(fl"1 , ff fl ( "'% ' & / 2/ fl!(fl ff ') & fl 2ffl '% , ' 1 " fl6 & )"fl& fl. &fl ff fl!(fl) * " ' &fl ffi fl fl)" , / " 'fl , ffl + ' &fl '% fl #1 .
31 *) " *" , " 1 ') ,") (" * "!(fl'% : m *D ; m *D f 2 1 ') *D m T 2 5) * " ( ( " 'fl 1ff 2 fl ! ,( !(fl"1 . 2 ff ) # " *"& , !- !(fl" 'fl # 1ff , (& "fi "fi fl " *"!(fl "1 & ff F bv d ffi b ' # fl !(fl * "' ( (Damping constant). ,(fl/ !(fl" 'fl 1ff 2 ) * " fl ! !(fl ,( , , 2ffl, 'flfl , ) , fi) flfl / !(fl) * "/ flffl ff +)fl. fl , !- !(fl*), ( / flffl ff +)fl. , (fi) flfl / 1 2 # ,fi ( ,( 'fl 1ff /4 ) * "/6ff &fl ff fl. * " *) 'fl& ,") fl " ,( " : * " ( (. % * " ( (' : / 2 ( ) sin bt m m xt xe t " *"!(fl * "/' : 2 2 4 k b f m m , 2 2 1 4 , 2 2 4 kb m m f T m m kb / % *), ( /,ffl " *) /fflff +)fl& & ) ,( ffi # , & ,") ') fi)flfl !(fl /ffl # ff +)fl ". 6) * ""ff ,fi (# 2ffl * "'( ffl +, * " ( (, ,fi *ffl " 'fi) flfl , *( 1ff " -(flfi) flfl 2ffl ' * "ffi# 2ffl,") ("!(fl * " 'fl. * " '" ,( " : * "" . ff 7) * " fl ,fi (2ffl * " # (2) - fl " fl ' 2 " 'fl fi ( 2 ) , (". ,fi ,( * " , ! fi 2& !(fl" 'flfi ( , ("" * " fl . ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
32 " 'flfi ( 2 ) * " : 0 0 FF t sin 2*),") (# ,( " : *),) & * "!(fl) #, & ( !(fl*), ( (,fi !& ) # ) ffl +fl/ *),) &, *) !(fl * " # 'fl ') " *" !(fl * " fl , " *" 0 !(fl'flfi ( , ,") * ", *) & . % * "' : xA t sin( ) ffi 0 2 2 2 2 0 F m/ A b m ffl ff fi ! " ') 0 m k fl !(fl*) ff * " fl * , (" *" !(fl" 'fl fi ( , " *" ,fi 0 !(fl) * " 0 , ,(" : * " ( fl)". 3. ( flfi : ' 7, " ') (3 "! (fl. , (ff (: - )# # ; (" 1 -ff !- 10g, 20g, 50g, 100g; , )fl!- ( ') * ' " ' , ffifl/ ,") , (* ,/ ,fi (, , ) * " , (,ffl + ( . - '%,/ ! "( ffl + '& 4.1 ffl 4.10. 4. / # ') ( / # 1: fi # " 3 " ') % * " "ffl +fl/ # 2ffl ,ffl *" * " " ffl+ ,fi ') '&),fi) "'& &fl ff fl, " 'fl fl &fl ff fl& % 4.1 / / fl ,!# 24 . / # 2: 'fl 4.1 ffl+ ffi,( )# # 2 " 1 ')ff ", 2ffl "1 ff * " ,fi (fi ffl " 'flffl 6 !(fl)# # 2 " 1 , / ff 1( #
33 * % " *" , " 1 ') ,") ("!(fl * "!(fl) * ") # # ') fi(" ,- # 4.2 ') 4.3 ,fi (2ffl ,ffl ) # )# # &# , )') "fi ( fi ffl # ffl 6 )"!(fl)# # 2 ) # &# )# # ' ) ') &# '!- . / # 3: 'fl 4.4 ffl+ ffi,( , ( )fl (3 " 1 ff - ') ", 2ffl * " * % &fl ff fl ,fi (fi ffl " 'fl fl "1 ff &fl ff fl, / 1(* # *) " *" , " 1 ') ,") ("!(fl) * " ". / # 4: 'fl 4.5 ffl+ ffi,( (" 1 ff- ,/ - fl ')",( ,ffl + ( (2 & )"fl(,fi (, 2ffl (" 1 ff- * "* * , / # " 2 # ffifl" 'fl,fi (fi ,( ffifl" 'fl 2 " 1 ff- , 2ffl * " ') 1(* *) " *", " 1 ') ,") ("!(fl) * " fi (" # 'fl2ffl,ffl ,1fl" '& & fl)ffl" fl) * " " ') ) * " . / # 5: 'fl 4.6 ')" fi # " ffi fl" 'fl 2 / ,fi (2ffl* *) " *" , " 1 ') ,") ("!(fl * ", fi (" # 2ffl ,ffl " 2 # ) * " 2 "/ "# ffl fl' . / # 6: ') " * "& "/ fl ') 2ffl ,ffl " * "2 # ) "'& , * " ( ( fi( , (2& ',fi (2ffl ,ffl *" * " ( ( *) fflff +)fl& & ) !(fl, # ) )# fl , fl " *" , " 1 ') ,") ("*) * & (4.11) fi( 'fl 4.7 2ffl ,ffl,1fl ( (!(fl * ". / # 7: ') " ,fl (*!,fi (# 2ffl * " , ( (, ffi & '')" ffl ff +*,1 fl * "" ff ') * "' fl ') 1(* *) !(fl * "' fl ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
34 ! " *" !(fl'flfi ( ') , * " ( fl)", (" *" !(fl'flfi ( , " 1 !(fl # * ", 'fl 4.10 ') 4.11 fi(( . 5. " ') ,% fi / ) / : - " 2/ ') 1 !(fl # . - " ,ffl !(fl . - ( 4 !(fl 2 & / . # - " "2'& ) / !(fl # '& ) . - " 1 & (fl!(fl # ,ffl ') ' ,) & "6 fl ') ,B ffl. ,B ffl 2ffl ' ,B ffl ! # 1 ffl !# 13. ' # ' ,B ffl 1. ,") ("!(fl) * " " T 2 g 2 M E ME E M EM 9 T ggT T g gT ffl ff fi ! " 2. ,") ("!(fl) * " " 2 2 2 4 gT T g 2 2 2 1 2 1 2 2 22 444 gT gT gT fl 2 2 1 2 T TT 2,5s 3. " *" fl ff max , k v A m max 0, 4m m A v k 4. ,") ("!(fl) * ") # # 2 2 4 2 m m T k k T 2 &# )# # ' " '!fl)" *) / 1 2 111 kkk 2 2 2 1 2 2 2 2 22 1 2 0,5s 444 T T T T TT fl
35 O kx cos kx sin mg F kx R 0 x 5. " 1!(fl) * ")# # 2 2 1 2 2 2 1 2 1 2 4 k k m f f m m f mf 2 1 2 1 2 2 0, 26kg f m m f 6. . " 1!(fl) * ")# # 1 0,8Hz 2 k f m - " *" fl ff max v A ; , fl 5rad/s k m max v A 0,5m/s - " ,)fl2ffl ff !(fl"1 ff * ". 2 2 max a A 2,5m/s !. ,( x 5cm, " *"!(fl * " 2 2 v Ax 1,12m/s " ,)fl!(fl"1 ff * " 2 2 a x 1,25m/s 7. # ffl 6 !(fl)# # / F kx 0 0 0 0 1000N/m F k x - *) )"fl "!(fl) # # 2 # , ",& 0 cos 60 F kx mg y 0,02m cos 60 mg x k 0 x 20 2 22cm - *) " 1 !(fl . 2 # , ",& 2 sin 60 F ma kx m R x C R sin 60 , 2 f 1 1,52 2 kx f m (/s 8. *) " M, 2 # " 1!(fl) * ")# # 2 2 1 2 4 k k f m m f 2 1 2 2 M m f M f 2 1 2 2 1 162g m f M M f ffl ff fi ! " - " '!fl!(fl)# # 2 2 1 k fM 4 162N/m ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
36 m1 m2 1 2 2 h 1 h 9. % * "' " 2 2 2 0 d x x dt # ,ffl " 2 2 2 2 6 72 0 12 0 dx dx x x dt dt fl 12 rad/s - ,") ("!(fl * " 2 T 1,8s - " 1!(fl * " 1 1 0,55Hz 1,8 f T 10. ,") (" * "!(fl) * " : 2 I T mgd 2 2 2 0,075kgm 4 mgdT I 11. 2 # , fi) flfl / 1122 2 2 11 1 1 2 2 2 2 1 1 2 2 EE E E E kPk k E m v m gh m v m gh 2 2 11 1 2 2 2 (1 cos ) ; (1 cos ) 2 2 h h ffi ffi ffi ffi ')" *" 11 2 2 v v ffi ffi ', ', ' /* : 2 2 2 2 11 1 1 2 2 2 2 1 1 ( ') ( ') 2 22 2 E m mg m mg ffi ffi ffi ffi ,( %& ) 2ffl # % , fl fl (fl! fl* : 11 2 2 2 2 2 11 2 2 '' g 0 '' 0 m m m m ffi ffi ffi ffi ' % * " ", , fl 11 2 2 2 2 11 2 2 g m m m m
37 1 x 2 x x x A A1 A2 , 1 p 1 p 2 p , 2 p , p p 1 2 5 * "' " ,") 3 "ffifl 1. /ff fl 2ffl , , ,! 2/ ') // *# : * "' "2 ) # & fl3 , : * " ")"fl ffi" *" , , * " ")"fl ffi " *" & fl , * "& )"fl& fl " *" , ') * "& )"fl& fl " *" & fl . 2ffl : - fl* % * "' "2'& ) ) # . - '&'%" ," ,&!(fl*) * "' ". - 2 # ,fi (*) *) )"!(fl * ", , (# fl)" ') % )"!(fl * "' "2'& ) ) # . 2. ,(2& & # ffl+ ( : ,(" 1 2- ff fl ,# * "ffl + (fi ( , ,( fl)"!(fl" 1 ff/' % " * "fi " ffi1 " fi" # fl% (& # . 1. fl)" (fl * "& )"fl" ') " *" , % *) ,( 11 1 xA t sin( ) ') 22 2 xA t sin( ) & ffl+ !(fl ( % * " fl)"' 1 2 sin( ) r x xx A t r x '*), ( fl)"!(fl (fl * "; A '*) fl)"!(fl * " ' , ,) &!(fl * " . 2 2 1 2 12 2 1 A A A AA 2 cos( ) ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
38 1 12 2 1 12 2 sin sin tan cos cos A A A A fi / ) 2 )# : . ,( 2 1 0 ffl+ ," *" 1 x ') 2 x , fl . # 2ffl 1 2 0 . /* 1 2 ( )sin r x AA t 'fl" , ( fl ", ,( * "' ", fl " *" # 'fl')*) , A1 A2 . !. ,( 2 1 ' ) # 1 x ') 2 x , . # 2ffl 1 0 ') 2 . /* 1 2 ( )sin r x AA t 'fl" , ( )"fl fl, ,( * " " " 1 , '& " *) fl)", AAA 1 2 . 2. fl)" (fl * "& )"fl" , '&" *" & fl 2ffl (fl * " , ,) & , 1 2 0 , % *), ( 1 1 x A t sin ') 2 2 x A t sin , , & fl 1 2 t /# fl , fl ," ,&" *" 2 )"/# fl . % )"!(fl * " r 1 2 x x x /# , * "' "( . *) )"!(fl (fl * "' : 2 2 1 2 12 1 2 A A A AA t 2 cos( ) ) # 12 12 t n AA A 2 ) # 12 12 t n AAA 2 1 ,( A A 1 2 /* 12 1 1 2 (sin sin ) r x xx A t t 12 12 1 2 cos( ) sin( ) 2 2 A t t ffl+ 1 mod 2 cos sin r av x A tt mod ( )sin At t av
39 2 av ' " *" ,) ') mod ' " *" !(fl * "" 1 fl (Modulation) fl : 2 21 av ') 1 2 mod 2 /,ffl*" * " "" *" ,) av . * " # , ' ", (fl/ " *) # fl ') *& ,") "" *" mod . 1 2 mod 1 1 1 2 ( ) 2 cos( ) 2 1 cos 2 A t A A tA t 'fl ( !(fl (fl , fl, ( * "' " "" *" '& & fl ,) (, , 2ffl, , (" : (beats). " 1!(fl 1 2 beat 1 2 2 f ff *) /, 'fl 1 12 1 2 cos 2 AA t )ffl" fl 0 ffl 2A. 3. fl)" * "& )"fl& fl , " *" , . "ff 1 ff- fl * "' "& ' x " % sin( )x xA t ') & ' y " % sin( )y yB t . # 2ffl * "- fl , ,) &, , & "6 fl2ffl 0 x , ,") y . /*: x A t sin ') yB t sin + ) # 0, sin y B t , /* fi "fi B y x A . + ) # , sin yB t , /* fi "fi B y x A . fl (fl ) # )" '& , % , *)ffl fl 2 22 22 2 2 2 2 2 sin B x r xy xx AB AB t A A % * "' " *) ': 2 2 A B ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
40 + )# , sin cos 2 2 y B t Bt ffl ff fi ! " , /* fi "fi 2 2 2 2 1 x y A B , fl' % !(fl'() . ,( / 2 ') x AA t sin 'fl" sin 1 t . fl , / ff x A " *" sin y dy v B tB dt " *"!(fl(fi ff / ff x A /!- ' y ') , y v ') ) , 'fl" ( fi ff )fl ') )# fl, ( *& ,! ffifl. ,( 3 /2 ffl+ / 2 * , ( , '() '& ,! ffifl ') ,( A B '() / , " fl . & "6 fl2, fl , & fl3 2 ) # A B , flfi * 2, (fl "' Oscilloscope. 4. fl)" * "& )"fl& fl , " *" & fl . )# * "!(fl (fl * " "& )"fl& fl '& " 1 & fl % )" */ ( " , ) (Lissajous Figures) ,(" 1 2 '&)' , (& "!(fl (fl,) / ",& # , : 123 , , 254 , &. 3. ( flfi : ' 7, " ') (3 "! (fl. , ( (: ff '%,/ ! "( ffl + '& 5.1, …') 5.9. 4. / # ') ( / # 1: fi # " * "' " ') %*), ( !(fl * "' ", ffl+fl/ & "6 fl2ffl ,ffl ,1fl * " fl)"!(fl (fl * " "2 . / # ,- ffl+ ( ') "1(* % , ( )"!(fl (fl * " %" !(fl % *), ( !(fl'& ) * ".
41 / # 2: " " '!(fl * "' ,1 fl" *" ') )"fl!(fl * " , fl( / ') ( & fl . fl , , ( * " fl)"!(fl * "' / fl& (fl 2'&) ) # . / / fl ) # fl)" * "& )"fl" ') " *", , ,) & " '& '%" ," ,&!(fl," ,&*) !(fl * " 1 ') 2 fl 'fl 5.1, (fl2 '%" ," ,&1(* *) )" ') , (# fl)" (fl * ". ffl +fl/ & "6 fl (fl ) # % ) , (# !(fl (fl * ", 0 ') , ffi 'fl'%" ," ,&fl 5.2 ') 5.3 fi(1(* % )"!(fl (fl ) # . / # 3: " * "' ) # (fl * "& )"fl" '& " *" & fl , ,fi ( " 2 # ,( ) # %& fl!(fl, (# !(fl * " fl (fl, 0, 'fl 5.4 ')" fi # 1(,( & fl3, ffl +fl/ 'fl 5.5 ')"( ,1fl 'fl!(fl, 'fl2 ') ffl ff +2ffl ') ,! 2/,1fl" 12 ) # * " " *" & fl . / # 4: " * "' "2 ) # (fl * "& )"fl& fl '& " *" & fl & ', ffl+fl/ 'fl 5.6, 5.7 ') 5.8 ')"( ,1fl 'fl!(fl , 'fl2 ') ffl ff +2ffl ') ,! 2/. ffl+fl/ fi # ' ,B ffl& "6 fl. 5. " ') , % fi / ) / : - " 2/ ') 1 !(fl # . - " ,ffl !(fl . - ( 4 !(fl 2 & / .# - " "2'& ) / !(fl # '& ) . - " 1 & (fl!(fl # ,ffl ') ' ,) & "6 fl ') ,B ffl. ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
42 ,B ffl 2ffl ' ,B ffl ! # 5, 6, 7, 8, 9 ') !# 10. 5. &(: ! # # fl 1 & (fl / : 2 2cos(20 / 6) 2sin(20 ) 3 xt t fl 12 1 2 2cm, =0, rad 3 A A *) fl )" ff 2 2 1 2 12 2 1 A A A AA 2 cos 2 3cm , (# )" 1 12 2 1 12 2 sin sin tan cos cos A A A A 3 rad 3 3 6. &(: ! # # 1 & (fl / : xt t 2 4cos( / 2) 4sin fl 1 2 12 A A 3cm; 4cm, =0, rad *) fl )" ff 2 2 1 2 12 2 1 A A A AA 2 cos 1cm , (# )" 1 12 2 1 12 2 sin sin tan cos cos A A A A 0 rad 7. 2 # % * "' " xA t tt t sin . 1 2 xt x t 6sin (cm); 3cos (cm) , 2 3cos 3sin , rad 2 xtt ffl ff fi ! " , fl 1 2 12 6cm; 3cm, =0, rad 2 A A *) fl )" ff 2 2 1 2 12 2 1 A A A AA 2 cos 3 5cm , (# )" 1 12 2 1 12 2 sin sin tan cos cos A A A A 6sin 0 3sin / 2 1 3 tan = rad 6cos0 3cos / 2 2 20 % * "' " 3 3 5 sin cm 20 t x t ffl ff fi ! "
43 o A1 A2 A3 A A A 3 2 !. 1 2 4sin 2 (cm); 8sin 2 (cm) 2 6 xt xt ffl ff ffl ff fi fi ! " ! " , 2 rad , 1 2 12 4cm; 8cm, = , rad 2 6 A A *) fl )" ff 2 2 1 2 12 2 1 A A A AA 2 cos A 4 3cm , (# )" 1 12 2 1 12 2 sin sin tan cos cos A A A A 0 0 % * "' " xt 4 3 sin 2 cm t . 1 2 3sin 2 (cm); 3sin 2 (cm) 3 6 xt xt ffl ff ffl ff fi fi ! " ! " , 2 rad , 1 2 1 2 3cm 3cm ; rad 3 6 A A # # $ $ % % $ $ & & *) fl )" ff 2 2 1 2 12 2 1 A A A AA 2 cos A 3 2cm , (# )" 1 12 2 1 12 2 sin sin tan cos cos A A A A 1 3 tan rad 1 3 12 % * "' " 4 3 sin 2 cm 12 t x t ffl ff fi ! " 8. , 2 3 1 12 3 1 2 3 3cm 7cm 3cm 1rad/s; ; ; 0 2 2 A A A xx x # # # $ $ %% % & $ $ & & % * "' " 123 sin( ) t xxxx A t ' 4 53 tan 3 180 ' ' / '%" ," ,&, & ffl + , & # 2 2 22 2 1 32 A A AA ( ) 3 (7 3) 25 A 5cm 53 5sin( )(cm) 180 t x t ສ.ວ.ສ ສະຫງວນລຂ ິ ະສດ ິ
44 o A1 A2 A x 1 2 x2 cm 4 3 4 3 O 20 10 3 20 5 t(s) 9. , : 1 2 1 2 2 1 6 3cm 12cm ? 2 rad/s; ; ; ? 3 6 A A A x xx # # $ $ # % %% & $ $ & & '&'%" ," ,&, / ffl + & ) # cosin: 2 22 21 1 1 2 2 cos 6cm A A A AA A ffl+ & ) # cosin: 2 22 12 2 2 A A A AA 2 cos 2 22 1 cos cos 60 60 30 2 6 / '%" ," ,&,ffl " , ,) & 2 , ) . fl 2 6sin(2 )(cm) 6 x t 10. * "!(fl" 1 ff m ' * "' ", fl xxx A t t tt 1 2 sin / fi) flfl , , ( fl ff 2 2 max max 1 1 6(cm) 2 2 E mv m A A k tt , 2 22 1 2 12 2 1 2 cos A A A AA t 2 A 4 3cm. fl , 2 4 3 sin 20 (cm) 2 x t ffl ff fi ! " / 1 12 2 1 12 2 sin sin tan 3 cos cos t A A A A 3 t % * ")"!(fl (fl * "' : 6sin 20 (cm) 3 t x t ffl ff fi ! " '& $ 'fl 2 ( ,) x t , fl 2 4 3 sin 20 (cm) 2 x t ffl ff fi ! "