Fisica General
April 10, 2023 | Author: Anonymous | Category: N/A
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Xjivhrsi`k` Jkciajkd Kut° ajagk ajagk `h Baj`urks Cui`k` Xjivhrsitkrik Hscuhdk Hscu hdk `h L°Ļsick Ļsi ck
@hpkrtkghjta `h Gkthrik Caj`hjsk`k
EX° IK @H HSPX@IA ^KVK ^VXHFKS HS^HCIKDHS ^VIGHVK XJI@K@? ASCIDKCIAJHS LISICK EHJHVKD II LS6>>
Suphrvisk`a par? GSc.Gkrdaj Okvihr Ijthrikja Hdkfark` Hdkf ark`a a pa par? r? Asck Asckr r Kjtaji Kjtajia a Kdc° k kjtkrk jtkrk Va Va`ri `rieu° eu° h hz z
Pheuciekdpk, Lrkjcisca Garkz°kkj, j, Baj`urks C.K.
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Asc Ascidk idkcia ciajhs jhs Kgar Kgartie tieuk` uk`ks ks y L Larz arzk`k k`kss
;.;.. ;.;
Ascidkc Ascidkciaj iajhs hs Kgarti Kgartieuk euk`ks `ks
Das sisthgks ascidkjths i`hkdizk`as quh bkstk kbark bhgas vista ja tihjhj lricci°aj= aj= ja bky luhrzks ja cajshrvktivks, dk hjhre°ĻĻkk ghc°kjick kjick tatkd tatkd hs caj cajstk stkjt jthh y uj sisthg sisthgkk puhsta puhsta hj gavig gavigihj ihjta ta sie sieuh uh ascidk ascidkj`a j`a hthrjk hthrjkghj ghjth th sij `isipk`arks, y `isgijuci° aj aj `h dk kgpditu`. Sij hgfkrea, das sisthgks `hd guj`a rhkd sihgprh tihjhj luhrzks `isipk`arks, dks ascidkciajhs chskj caj hd tihgpa, k ghjas quh uj ghckjisga rhpajek dk hjhre° hjhre°Ļk ghc°kjick kjick `isipk`k. Hd ga`hda `h uj ascidk`ar ghc°kkjica jica saghti`a hxcdusivkghjth k dk dhy `h Baamh ja hs rhkdistk puhs `hsprhcik dk prhshjcik `hd razkgihjta. Dk hxphrihjcik jas guhstrk quh uj ascidk`ar sh vk lrhjkj`a praerhsivkghjth bkstk ddhekr k `hthjhrsh hj dk pasici°aj aj `h hquidifria. Hstk `isgijuci°aaj j praerhsivk hj dk kgpditu` `h dks ascidkciajhs hs `hfi`k k dk prhshjcik `h Kgartieukgihjta. Dk `isgijuci°aaj j `h dk kgpditu` ckusk`k par luhrzks `isipk`arks sh `hjagijk ° kgartieukgihjta,, y hd gavigihjta carrhspaj`ihjth sh ddkgk ascidkci° kgartieukgihjta aj aj kgartieuk`k. kgartieuk`k. Hsth kgartieukgihjta puh`h `hfhrsh k uj rach caj ujk suphrcih a dk lricci°aaj j `hd kirh a d°Ļqui`a quh ra`hk kd ascidk`ar. ^ar da ehjhrkd hd kgartieukgihjta sh `hfh k dk rhsisthjcik `hd kirh y k dk lricci°aj ijthrjk `hjtra `hd sisthgk ascidkjth. Kujquh hd kgartieukgihjta kdthrk dk lrhcuhjcik `h dk vifrkci°aaj, j, hd hlhcta hs usukdghjth phquh˔ja ja si hd kgartieukgihjta hs phquh˔ ja. ja. ± ^ar qu°h bkfdkgas bkf dkgas `h gavigihjta gavi gihjta krg°ajica ajica sigpdh (ja kgartieuk`a)1 Dk rhspuhstk rhspuhstk hs quh hd GKS hs gucba g° ks l° kcid `h trktkr gkthg° ktickghjth = y si hd kgartieukgihjta ja hs erkj`h (ashk `hsprhcikfdhs), dks ascidkciajhs sh puh`hj cajsi`hrkr caga gavigihjta krg°ajica ajica sigpdh, safrh hd cukd sh suphrpajh hd kgartieukgihjta. Hd sisthgk ascidkjth quh kbark kjkdizkgas kct° uk uk safrh hd ujk luhrzk k`iciajkd= hstk luhrzk k`iciajkd dk ddkgkrhgas Luhrzk `h kgartieukgihjta dk kgartieukgihjta dk cukd `hphj`h `h dk rkpi`hz `hd afohta ascidkjth y sh apajh kd gavigihjta `hd gisga. Dk luhrzk `h kgartieukgihjta puh`h kpraxigkrsh caga ujk luhrzk `irhctkghjth praparciajkd k dk rkpi`hz? L kgartieukgihjta kgartieukgihjta 7 – fψx
(;)
@aj`h f hs dk cajstkjth quh `hscrifh dk ijthjsi`k` `h dk luhrzk kgartieuk`ark y hd sieja ghjas ij`ick quh dk luhrzk sihgprh tihjh `irhcci°aj aj apuhstk k dk vhdaci`k`. L x 7 L kgartieukgihjta Kbark Dk luhrzk tatkd quh kct°uk uk safrh hd sisthgk hs kgartieukgihjta + L Baamh Baamh , y sustituyhj`a das rhsphctivas vkdarhs `h dk hcukci°aaj j` `hh dk `hrhcbk jas `kr `kr°°Ļk hjtajchs? h jtajchs?
L x 7
∖fψx–οx
(6)
οx,, dk luhrzk rhstkurk`ark `hd rhsarth (Dhy `h Baamh)= ο hs dk cajstkjth `hd rhsarth y x @aj`h hd thrgija thrgija οx y x hs dk dajeitu` `h dk cagprhsi°aaj j a kdkrekgihjta `hd rhsarth. @k`a quh hs uj sisthgk hj gavigihjta hd quh kjkdizkgas jas rheirhgas safrh dk sheuj`k dhy `h Jhwtaj?
∖
gkx 7
∖fψx–οx
(3)
aj `ilhrhjcikd, Kbark rhkdizkrhgas ujk gkjipudkci°aaj j kdehfrkick pkrk hxprhskr dk hcukci°aj aj (3) caga ujk hcukci°aj rhkdizkj`a dk sieuihjth sustituciajhs?
Li Lieu eurrk ;? Gavig vigih ihj jta `hd `hd as asci cidk dk`a `arr kga gart rtie ieuk uk`a `a
Li Lieu eurrk 6? Gavi vig gih ihj jta kr krg gajica °ajica sigpdh
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6
kx 7 ``t6x ψx 7 `x `t Kpdickj`a dks sustituciajhs kjthriarghjth ghjciajk`ks ,hxprhskj`a hd prighr thrgija `h dk izquihr`k sij cahrhsudtk caga? caga? cihjths y `hokj`a hd thrgija `h dk `hrhcbk caga ieukd k chra, dk hcukci°aj (3) rhsudtk `6 x f `x ο + + x 7 > `t6 g `t g
(0)
Hstk hcukci°aj, aj, hs dk hcukci°aj aj `ilhrhjcikd `h gavigihjta `hd ascidk`ar krg°aajica jica caj uj thrgija `h kgartieukgihj f `x
ta= ja afstkjth jath quh sij hd thrgija hxtrk sigpdh.
g `t shrik
ieukd kdk hcukci°aaj j `h gavigihjta `hd ascidk`ar krg°ajica ajica
^hra kuj vkdh `hstkckr ujk udtigk ga`ickci°aj, aj, hsta k gkjhrk `h `htkddkr `as cajstkjths `h sugk igpartkjcik, pkrk dk ijthrprhtkci°aj aj `h dk saduci°aaj j gkthg°ktick ktick ks° ks°Ļ caga pkrk `htkddkr dk saduci°aaj j l°Ļsick, k cajtijukci°aaj j gastrkrhgas hstk udtigk ga`ickci°aj aj kdk hcukci°aj aj (0)? `6 x `x ζ + ω>6 x 7 > + 66ζ 6 `t `t
(8)
aj, pa`hgas jatkr quh hstas juhvas t° hrgijas hrgijas hj Hj dk hcukci°aj aj (8) quh hs dk rhsudtkjth `h hstk udtigk ga`ickci°aj, dk ga`ickci°aj aj saj `as, das cukdhs saj cajstkjths? ο ω> 7 g hs dk lrhcuhjcik prapik `hd ascidk`ar y ja hs dk gisgk quh dk dk ω pkrk hd GKS sij kgartieukgihjta. Y hstk hquivkdh k dk lrhcuhjcik jkturkd caj dk quh ascidkr°Ļk Ļk hd rhsarth si ja tuvihrk razkgihjta (caga sh bkf° bkf°Ļk `htkddk`a `htkddk `a kjthriarghjth).
ζ ζ 7 6fg hs dk cajstkjth `h kgartieukgihjta. kgartieukgihjta. Gi`h dk gkejitu` `h dk lricci°aaj, j, sihj`a gkyar cukjta g° ks ks ijthjsk ijthj sk shk °hstk. hstk . ζ pashhj Pkjta dk lrhcuhjcik prapik `hd ascidk`ar ω ascidk`ar ω > caga dk cajstkjth `h kgartieukgihjta ζ pashhj dks gisgks `ighj∖ ; siajhs y sh gi`hj hj Bhrtz (Bz) °a ijvhrsk `hd tihgpa (s ( s ). Kjths `h hxkgijkr dk saduci°aj aj gkthg°kktick tick `h dk hcukci°aaj j `ilhrhjcikd `hscritk hj dk hcukci°aj aj (8), pa`hgas `hscrifir caga `hfhr° `hfhr°Ļkj shr dks saduciajhs `k`a hd cagpartkgihjta l°Ļsica Ļsica `hd sisthgk. @hscripci°aj aj `h dks Saduciajhs? Si hd kgartieukgihjta hs phquh˔ ja, ja, `hfhgas hsphrkr quh hd rhsarth ascidh pkra caj ujk kgpditu` `hcrhcihjth, bkstk quh pksk`a uj cihrta tihgpa sh quh`h hj rhpasa hj dk pasici°aj aj `h hquidifria. Si hd kgartieukgihjta hs guy erkj`h, hj ckgfia, hsphrkgas quh ja ddheuh k ascidkr, sija quh sigpdhghjth sh vk gavihj`a dhjtkghjth bkstk dk pasici°aj aj `h hquidifria. Pagkj`a hj cuhjtk da hxprhsk`a kjthriarghjth, vhgas uj cihrta pktr°aj aj cajcihrjh kdk gkejitu` `hd kgartieukgihjta= par da quh bky ujk cagpkrkci°aj aj `h vkdarhs hj ujk hsckdk quh puh`h tagkr hsth kgartieukgihjta y caga hsta klhctkr° klhctkr°Ļk k juhstrk sisthgk= hj dk l°Ļsick Ļsick sihgprh quh ujk gkejitu` sh cajsi`hrk erkj`h a phquh˔j jkk bky quh `hcir hd parquh, cu°kd kd hs hd pktr°aaj j hj quh jas fkskgas pkrk `hcir si kdea hs erkj`h a phquh˔ ja. ja.
Lieurk 3? Ascidk`ar kgartieuk`a
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ζ caga Hj hsth cksa uskrhgas dks `as cajstkjths hjcajtrk`ks hj dk hcukci°aj aj (8) quh saj tkjta ζ caga ω> , dks cukdhs tihjhj dks gisgks `ighjsiajhs y par tkjta sh puh`hj cagpkrkr hjtrh si y k`hg°kkss `h quh kgfks ouhekj uj pkphd igpartkjth hj dk hcukci°aj aj `h gavigihjta. Hstkfdhzckgas hd crithria safrh hd cukd hddas puh`hj shr gh`i`as? ζ 4 ω > Kgartie Kgar tieukgi ukgihjta hjta `°hhfid? fi d? ζ Kgartieukgihjta luhrth a ijthjsa?ζ ijthjsa?ζ : ω > Y par da tkjta dk saduci°aaj j gkthg°ktick ktick `hfh rhsthokr uj ckgfia `h cagpartkgihjta `hphj`ihj`a `h caga shk dk cajstkjth `h kgartieukgihjta kd shr cagpkrk`k caj dk lrhcuhjcik prapik `hd ascidk`ar. Hsta sh vhrk `h gkjhrk gks cdkrk cukj`a vhkgas das cksas `h kgartieukgihjta, caj su rhsphctivk `hscripci°aaj j er°kck kck `h das gisgas pkrk `kr ujk ghoar ijthrprhtkci°aj aj k da quh sh `hjici°aj aj caj kjthriari`k`. ^rasheuigas k rhsadvhr dk Hcukci°aaj j `ilhrhjcikd, `hjatk`k hj dk hcukci°aj aj (8 ( 8), phra ja hjtrkrhgas gucba hj `htkddh ° K, K, kchrck `hd g°hta`a hta`a `h rhsaduci r hsaduci°°aaj j `h hstk hcukci°aj aj `ilhrhjcikd dk cukd quh`krk hxprhsk`k hj hd K^HJ@ICH par cajsieuihj cajsieuihjth th sada gastrkrhg gastrkrhgas as hd rhsud rhsudtk`a tk`a `h dk gisg gisgk? k? x(t) 7 c; hk; t + c6 hk6 t
(6
ζ 6
∖ ω>6
Caga sh hxpusa kjths `hphj`ihj`a `h caga shk hd vkdar `h dk cajstkjth `h kgartieukgihjta (ζ ( ζ ) caj rhsphcta kd vkdar `h dk lrhcuhjcik prapik `hd ascidk`ar (ω (ω> ), hxistir°kj kj caga tkd trhs pasifidi`k`hs a hj atrks pkdkfrks trhs cksas `h caga shrk hd cagpartkgih cagpartkgihjta jta `h juh juhstra stra sisthgk ascidk`ar= hsta vista k trk trkv° v° hhss `h da quh pra`uzck dks cajstkjths k; y k 6 , thjihj`a hj cuhjtk dks cajsi`hrkci°aj aj `hd vkdar `h `h ζ y y hd sieja quh pra`uzck da `hjatk`a hj 6 6 ω> ). dk hcukci°aj aj `hjtra ` hjtra ` `hh dk rk° rk°Ļz ccuk`rk`k uk`rk`k (ζ
∖
Cksas pasifdhs `hd sisthgk sisthgk ascidk`ar? ascidk`ar? ζ : ω> dks `as saduciajhs saj rhkdhs y `ilhrhjths (cksa safrhkgartieuk`a). Si Si ζ ( cksa safrhkgartieuk`a ). rtieuk eukgihjt gihjta a cr°Ļtica Ļti ca). ζ 7 ω> hxisth ujk saduci°aj aj rhkd `afdh (kga (kgarti ). Si Si ζ 7 ω ζ 4 ω> dks `as saduciajhs saj cagpdhoks cajouek`ks (cksa sufkgartieuk`a). Si Si ζ ( cksa sufkgartieuk`a ). ;.;.;. ;.;. ;.
Cksa sufkga sufkgarti rtieuk euk`a `a (ζ 4 ω > )
Hsth cksa da afthjhgas afthjhgas cukj`a hd razkg razkgihjt ihjtaa hs `° hhfid= fid= par da cukd shrk jhchskria jhchskria hgpdhkr dks `hjiciajh `hjiciajhss `h dks cajstkjths k; y k6 dks cukdhs hrks dks saduciajhs `h juhstrk hcukci°aaj j `ilhrhjcikd hxprhsk`k hj dk hcukci°aj aj (0).
∖
∖
k; 7
∖ζ + + k6 7 ∖ζ ∖
∖ ∖ ζ 6
ω>6
ζ 6
ω>6
^ar cajsieuihjth pkrk t°hrgijas hrgijas `h sigpdickci° aj aj y k gkjhrk `h `hjatkr ujk juhvk hxprhsi°aaj, j, `hjirhgas ujk juhvk juh vk vkrikfdh vkrikfdh caga tkd `hjatk`k par dk dhtrk ω dhtrk ω ? ω 7
∖ ω>6
ζ 6
(5)
Dk cukd sh `hjh caga dk lrhcuhjcik kjeudkr `hd ascidk`ar caj pack lrhcuhjcik. Yk caj hstk juhvk vkrikfdh, pa`hgas hscrifir dks `as saduciajhs `h dk hcukci°aj aj (0) caga cagpdhoas cajouek`as, `k`a quh hd vkdar quh hxisth kbark hj dk rk°ĻĻz, z, shrk uj vkdar jhektiva, par da cukd vkgas k rh-hxprhskr hd vkdar `h dks cajstkjths. k; 7 k6 7
∖ζ + + iω ∖ζ ∖ iω
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∟ ∖
Sihj`a i 7 Sihj`a i ; dk uji`k` igkeijkrik. ^ar da tkjta juhstrk saduci°aj aj `h dk hcukci°aaj j `ilhrhjcikd hcukci°aj aj ( ? sada gastrkrhgas dk largk jkd `h dk hcukci°aj aj quh `hscrifh hd gavigihjta fkoa dk rhstricci°aaj j `h `h ζ ∖ ζt x(t) 7 Kh ω t + Ϙ) cas(ω cas( ζ rhcar`hgas Y hstk hs dk hcukci°aj aj `h gavigihjta `hd ascidk`ar caj paca kgartieukgihjta, `aj`h ζ rhcar`hgas hs pa`hgas dhhr hstk saduci°aj aj caga ujk ascidkci°aaj j sijusai`kd? x(t) 7 K > cas cas (ω t + Ϙ)
(;>) f 6g =
y
(;;)
Caj ujk kgpditu` dk cukd `hckh hxpajhjcikdghjth, hd cukd hstk `hjatk`a par K > 7 Kh 7 Kh∖ζt . ^krk pa`hr `hjir a hxprhskr caga tkd hd cagpartkgihjta vista `h largk er°kck, `hjirhgas da quh hs uj gavigihjta gavigihj ta cuksiphri° cuksip hri°a`ica? a`ica? Xj gav gavigihj igihjta ta cuksiph cuksiphri° ri° aa`ica `ica hs hd tipa `h hvaduci°aj aj thgparkd quh prhshjtk uj a`ica rhpith a`ica rhpith ujk y atrk vhz caj`iciajhs krfitrkrikghjth chrckjks k ujk pasici°aaj lhj° aaghja ghj a l°Ļsi Ļsica ca quh sij quh sij shr phri° j prhvik `hd sisthgk. Xj lhj°aghja aghja cuksiphri°aa`ica ascidk `ica ascidk ujk ujk y atrk vhz gastrkj`a ck`k cihrta tihgpa uj ksphcta sigidkrr kd quh tuva hd sisthgk sigidk sisthgk prhvikghj prhvikghjth. th. a`ica, a`ica, ^ar da tkjta hd cagpartkgihjta er°kca kca quh prhshjtk hd cksa sufkgartieuk`a sh `ich quh hs cuksiphri° parquh ja ddhek k rhphtirsh (kd cagpdhtkr ujk ascidkci°aj aj ja sh hjcuhjtrk hj dk gisgk pasici°aaj j quh kd ijicikrdk). Hd cuksiphria`a hs gkyar quh hd `hd ascidk`ar sij kgartieukgihjta(caga sh afshrvk hj hd er°kca kca `hd Ascidk`ar sufkgartieuk`a (ζ (ζ 4 ω> ))= thjihj`a hj cuhj cuhjtk tk dk sieuih sieuihjth jth krgkc krgkci° i°aaj j afthjhgas dks sieuihjths rhdkciajhs? ω 4 ω> 6ώ 6ώ P 7 : P > 7 ω ω> @aj`h P hs hd phria`a `hd ascidk`ar caj kgartieukgihj @aj`h P kgartieukgihjta ta `°hhfid= fid= Y par udtiga hd tihgpa quh tkr`k hj `hckhr dk kgpditu` ja das `k cajstkjth `h kgartieukgihjta ζ kgartieukgihjta ζ = Y hsth tihgpa sh `hjh caga? ; π 7 (;6) ζ
ζ 4 ω >) Lieurk 0? Ascidk`ar sufkgartieuk`a ((ζ
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Cksa safrhkg safrhkgart artieuk ieuk`a `a (ζ : ω > )
Cajsi`hrkrhgas Cajsi`hrkrh gas kbark hd Cksa safrhkga safrhkgartieu rtieuk`a= k`a= Hj hsth cksa juhstrks juhstrks `as saduciajhs saduciajhs pkrk dk hcukci° hcukci° aj aj (0), saj rhkdhs y kgfks caj vkdarhs jhektivas? k; 7 k6 7
∖ ∖ ∖ ∖ ∖ ζ + +
ζ 6
ω>6
ζ
ζ 6
ω>6
^ar da cukd saduci°aj aj `h dk hcukci°aj aj `ilhrhjcikd hxprhsk`k hj dk hcukci°aj aj (< ( 6
(;3)
Cksa caj kgartieukgihjta kgartieukgihjta cr°Ļtica (ζ 7 ω 7 ω > )
^ar udtiga thjhgas hd cksa `aj`h hd kgartieukgihjta hs critica= Hj hsth cksa hd sisthgk yk ja ascidk, sija quh vuhdvh k su pasici°aj aj `h hquidifria sij ascidkr cukj`a sh dh `hspdkzk y suhdtk. Hstk cksa hs uja pkrticudkr quh `hfh shdhcciajkrsh ga`ickj`a dks prapih`k`hs `hd sisthgk, yk quh rhquihrh ujas ω > , y `h hstk largk afthj`rhgas vkdarhs cajcrhtas `h das pkr°kghtras, kghtras, yk quh `hfh cugpdir caj dk caj`ici°aaj ζ j ζ 7 7 ω dk sieuihjth cajshcuhjcik? ζ 7 ω 7 ω>
⇖
f 7 6g
⇖ ο g
∟
f 7 6 οg
Y `k`k hstk cajshcuhjcik, afthjhgas hd vkdar `h dk cajstkjth cajstkjth f (dk cukd jas `hscrifh dk ijthjsi`k` `h dk luhrzk οg), kgartieuk`ark) y hd cukd `hfh thjhr hsth vkdar hxkcta (6 οg ), sihj`a hsth vkdar su vkdar critica. Si hd vkdar `h f ckdcudk`a a `k`a sh cagpkrk caj hd vkdar critica `h f, y hsth rhsudtk shr uj paca gkyar k hsth, yk hd gavigihjta hs safrhkgartieuk`a y si hs uj paca ghjar, hs sufkgartieuk`a.
∟
kqu°Ļ kpdickrhgas dk caj`ici° aj a j `h (ζ (ζ 7 ω 7 ω> ), hsta ^krk hsth cksa hj pkrticudkr, pkrtirhgas `h dk hcukci°aj aj (8) y kqu° ° HJ@ICH ICH K= par cajsieuihjth sada gastrkrhgas dk hcukci°aj quh`krk `htkddk`a hj hd K^HJ@ aj `h gavigihjta quh `hscrifh `hscr ifh hsth cksa hj pkrticudkr pkrticudkr
x(t) 7 (c; + c6 t) h∖ζt
(;0)
ζ : ω >) Lieurk 8? Ascidk`ar safrhkgartieuk`a ((ζ
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L°Ļsick Ehjhrkd I I
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Phjihj`a dk hcukci° aj aj `h gavigihjta, sh prasieuh k vhr su cagpartkgihjta Er°kca= afshrvkj`a quh hs hstk lujci°aaj j rhprhshjtk uj `hckigihjta hxpajhjcikd, sigidkr kd cksa safrhkgartieuk`a. Hd kgartieukgihjta kgartieukgihjta cr cr°°Ļtica p pashh ashh ujk prapih`k` quh da d a bkch ijthrhskjth ijthrhskjth `hs`h hd pujta `h vistk t°hcjica? hcjica? hs hd cksa hj quh sh rhtarjk g°ks ks r°kpi`kghjth kpi`kghjth k dk pasici°aj aj `h hquidifria. Si dk lricci°aj aj hs ghjar, hd ascidk`ar vk y vihjh y tkr`k g°kkss hj pkrkrsh. Si hs gkyar, dk luhrth lricci°aj aj rkdhjtizk hd gavigihjta gavigihjta y tkr`k tkgfi° hj hj g° ks ks hj pkrkrsh. ^ar hdda, das kgartieuk`arhs `h das kutag° avidhs avidhs y `hg°ks ks gkquijkrik pracurkj pra curkj koustkrsh k oustkrsh kd vkdar cr°Ļtica, Ļtica, yk quh `h hstk largk sh cajsieuh hd afohtiva `h `hthjhr dks vifrkciajhs hj hd ghjar tihgpa pasifdh. Hj largk `h cajcdusi°aj aj cajcihrjh k das trhs cksas kjthriarghjth `hscritas pa`hgas `hcir caj rhsphcta k hddas quh= hj gucbas sisthgks, hd gavigihjta ascidktaria hs da quh cuhjtk, caga hj das rhdaohs, y hd kgartieukgihjta `hfh gijigizkrsh. Hj atras sisthgks, dks ascidkciajhs saj hd prafdhgk, caga hj das rhsarths kutagatrichs, par da quh sh quihrh daerkr ujk ckj ckjti`k` ti`k` `h kgart kgartieukg ieukgihjt ihjtaa kprap kprapik`k ik`k (hs `hcir, `hcir, kgartieuk kgartieukgihj gihjta ta cr cr°°Ļtica). Ļtica). Xj kgartieukgihjta fihj `ish˔ j jk`a k`a hs jhchsitk pkrk ta`a tipa `h kpdickciajhs.
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