Pendulo Simple

 

Wcfvgrsfnin Aiykr ng Xic Icnræs Oihudtin ng Fclgcfgrái Dimkritkrfk ng Oásfhi

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RÆCNWDK XFARDG 9.9

KM@G^F_KX   Ngt Ngtgra grafci fcirr gxpgrfa gxpgrfagct gctida idagct gctg g di ihgd ihgdgrih grihføc føc ng di lriv lrivgni gnin n y

ngtgra ngtg rafc fcir ir di ghui ghuihf hføc øc ga gapá párf rfhi hi ng ngdd pg pgrf rfkn knk k ng kshf kshfdi dihf hføc øc ng ngdd pæcnudk.

9.=

OWCNIAGC^K ^GØ]FHK Wc pæcnudk sfapdg (Ofluri 9), hkcsfstg gc uci aisi ng nfagcsfkcgs ngsprghfimdgs suspgcnfni ng uc jfdk fcgxtgcsfmdg y ng aisi ngsprghfimdg. Huicnk sg sgpiri uc écludk  a  y sg dk sugdti, gd pæcnudk kshfdi idrgngnkr  ng gsti pksfhføc gc uc pdick vgrtfhid hkc uc akvfafgctk qug i di vgz gs pgrfønfhk. Gd pæcnudk kshfdi gc uc pgrfknk —^‑ qug vfgcg i sgr gd tfgapk gapdgink gc goghtuir uci kshfdihføc hkapdgti. Riri fcfhfir gd icédfsfs gdglfrgaks nks g`gs, uck gc nfrghhføc ticlgctg i di triyghtkrfi y gd ktrk gc nfrghhføc rinfid. Gc gd pdick isá okraink sg prgsg prg sgct ctir iric ic tk tkni niss di diss ou ougr grzis zis qu qug g ihtðic skmrg di aisi ngd pæcnudk gc gd fcstictg gc gd qug gs ipirtink ng su pksf pk sfhf hføc øc ng gq gquf ufdfdfmr mrfk fk uc pgqu pgqugù gùk k écludk — ‑‑..  Xf ngshkapkcgaks gd pgsk gc di nfrghhføc ngd g`g ticlgchfid i di triyghtkrfi tgcgaks0 \  Z     al sgc   

(9) Rkr tritirsg ng uc écludk auy pgqugùk0   ~   \  Z     al     Xfc  ~

(=)

Rkr dk tictk di pkdgi tfgcng i vkdvgr i su puctk ng gqufdfmrfk ngmfnk i uci ougrzi rgstiurinkri prknuhfni pkr di lrivgnin, qug tgcnré uc sflck cglitfvk sgré0  

 O  

\  Z 

 O  

 al  

(8)

 

Wcfvgrsfnin Aiykr ng Xic Icnræs Oihudtin ng Fclgcfgrái Dimkritkrfk ng Oásfhi

]gskrtgs

Hkak gd écludk — ‑ gs auy pgqugùk, sg isuag qug gd irhk qug ngshrfmg di aisi id kshfdir gs iprkxfainiagctg uc ngspdiziafgctk dfcgid0    Z     D   

(>)

 Rkr dk tictk tgcgaks0  O    

alZ   D

 

(7)

Nkcng sg pugng kmsgrvir qug di ougrzi rghupgrinkri —O‑ piri pgqugùks ngspdiziafgctks gs nfrghtiagctg prkpkrhfkcid i d gdkclihføc —x‑.    O     EZ  Xfgcnk

 (?)

, di ngckafcini hkcstictg rghupgrinkri goghtfvi ngd pæcnudk.

Di hkcnfhføc cghgsirfi piri qug gd akvfafgctk iraøcfhk sfapdg (AIX) gs qug sg ji jiddddg g skag skagtftfni ni i uc uci i ougr ougrzi zi rg rghu hupg pgri rink nkri ri qu qug g sgi sgi nfrg nfrght htia iagc gctg tg prkpk prk pkrhf rhfkc kcid id i di gd gdkcl kclihf ihføc øc y ng sg sgct ctfn fnk k kpu kpugst gstk. k. Gc cu cugst gstrk rk hi hisk sk gd akvfafgctk icidfzink huapdg hkc gstis hkcnfhfkcgs. Xf ipdfhiaks di sglucni dgy ng Cgwtkc i di aisi ngd pæcnudk tgcgaks0 

al      



 

ai

 

(   D

 l   ^ =

(9>)

(99)

 

Wcfvgrsfnin Aiykr ng Xic Icnræs Oihudtin ng Fclgcfgrái Dimkritkrfk ng Oásfhi

]gskrtgs

Di ghuihføc (9>) cks pgraftg ngtgrafcir di ihgdgrihføc ng di lrivgnin dkhid prgvfiagctg hkckhfnks gd pgrfknk y di dkclftun ngd pæcnudk. Hkak gs fapksfmdg gxpgrfagctir hkc uc pæcnudk sfapdg, qug ck gs cini ais qug uc akngdk fngid y hkak, nurictg gd ngsirrkddk ngd gxpgrfagctk sg utfdfziri uci pgqugùi gsogri agt agtédfhi édfhi qug gc rgid rgidfnin fnin ck gs uci aisi puctuid puctuid sfck uci uc i ai aisi si qu qug g pk pksg sgg g nfag nfagcs csfk fkcg cgs5 s5 di gsog gsogri ri ng ngmg mgré ré huap huapdfdfrr hfgr hfgrti tiss hkcnfhfkcgs piri qug gd pæcnudk gc gstunfk sgi hkcsfngrink —pæcnudk sfapdg‑. i) Aéxfak écludk ng sgpirihføc (   )  Ictgs ng n g fcfhfir di prihtfhi gs cghgsirfk ngtgrafcir huic pgqugùk pugng sgr  hkcsfngrink gd écludk ng sgpirihføc. Xf di iapdftun ng kshfdihføc ck gs pgqugùi, gd pgrfknk ngd pæcnudk gsti gc ouchføc ngd écludk ng sgpirihføc sglðc di sflufgctg gxprgsføc0 ^ 



 D

= 

 l 

(9  

6 9   =     sfc( )  ...........   sfc ( )  ?> = > =

(97)

Xf ngsprghfiaks dks tærafcks ng dis pktgchfis supgrfkrgs pkr sgr vidkrgs auy pgqugùks y hkcsfngriaks ðcfhiagctg dks nks prfagrks, tgcgaks0 ^ 



 D

= 

 

 l 

9     sfc = ( )) > =

(9  

 

Xf ngsirrkddiaks di sgrfg ng sfc (  

=

^ 



 D

= 

 l 

(9 

 

)  y

(9?) sg ngsprghfic dks tærafcks supgrfkrgs0

= 

9?

(9)

Ngspg`icnk di ihgdgrihføc ng di lrivgnin0 =

>   D(  l = 

=  ] =

7  D= ^ =

 9)

(=7)

Gd grrkr qug sg hkagtg gc di agnfni ng di ihgdgrihføc ng di lrivgnin id hkcsfngrir di aisi ng di gsogri hkak aisi puctuid sgré0 =

 l    l =    l    l ( =  ]= )

7  D

 

Wcfvgrsfnin Aiykr ng Xic Icnræs Oihudtin ng Fclgcfgrái Dimkritkrfk ng Oásfhi  l 

 l 

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=  ] =



=  ] = 7  D=

(=?)

7  D=

 G rl 



(= 9.>

Wci gsogri agtédfhi Jfdk fcgxtgcsfmdg Hrkcøagtrk ^krcfddk afhrkaætrfhk ]gldis

R]KH R]KHGN GNFA FAFG FGC^ C^K K GC GD DI DIMK MK]I ]I^K ^K]F ]FK K

(=:)

 

Wcfvgrsfnin Aiykr ng Xic Icnræs Oihudtin ng Fclgcfgrái Dimkritkrfk ng Oásfhi

]gskrtgs

 I) Ngtgrafcihføc ng di ihgdgrihføc ng di lrivgnin 9. Gd nkhgctg isflciri gd grrkr pkrhgctuid prgof`ink piri di ngtgrafcihføc ng di ihgdgrihføc ng di lrivgnin. =. Agnfr gd nféagtrk ng di gsogri y di dkclftun ngd jfdk (i (ipr prkxf kxfai aini niag agct ctg g . Agnfictg di ghuihføc (=), rgi rgidfzir gd prk prkhgsk fcvgrsk ng prkp pr kpil ilihf ihføc øc ng gr grrkr rkrgs gs y ng ngtg tgra rafc fcir ir gd gr grrkr rkr rg rgdit ditfv fvk, k, qu qug g sg ng ngmg mg hkagtgr gc di agnfni ngd pgrfknk. ?. Riri dis 9 92 2k ksh shffdihfkcgs, agnfr g gdd p pg grf rfk knk i ip prk rkxxfaink ^ ^,, rrgp gpgt gtffr  gd prkhgnfafgctk trgs vghgs y sihir gd prkagnfk. t  ^   cc  

   =  dc     dc  D  = dc ^ 

Nfogrgchficnk0

 l 

 l 



 D  

 D



=

^ 

^ 

 

 

Wcfvgrsfnin Aiykr ng Xic Icnræs Oihudtin ng Fclgcfgrái Dimkritkrfk ng Oásfhi

 D  D

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=

^  ^ 

*   G rl 

* ^   G rl  = 

^ 

 C 

* rl 

 G 

(2,297)

 G r^   = C  

 2,228

Agnfaks gd tfgapk ng 92 kshfdihfkcgs t92 92  1 9?.7(s) Gd pgrfknk iprkxfaink gs0 t  9?.7 ^ c   9.?7( s ) c 92 Gd C° ng vghgs qug ngmg kshf kshfdir dir gd pæcnudk sgré0 c c 87  Agnfaks ^87  1 7:.6>

^ 

t 87 87





g  G r^  * ^ 

87(vghgs )

7:.6> 87

 9.?:( s)

Kmtgcfgcnk gd grrkr ngd tfgapk y ng di dkclftun D0   ^1 9 ?: ¹ 2 29 s D1 2   D =

^ 

=



>  (