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"djalshmudjrphyslgs.la" :
D@KNSA YH\WLGW - :: YH@[@NONG[SLG NBBNG[ 6
Uhna nongtr djeantlg rjkljtl`as `b sultjcon wjvnonaeth jrn laglknat`a j dntjoolg surbjgn thna nongtr`as jrnndlttnk, thls phna`dna`a ls gjoonk ph`t` nongtrlg nbbngt.
:.: Yh t`nongtr a 6[hn nongtr`a ndlttnk la ph`t`nongtrlg nbbngt ls gjoonk ph`t`nongtr a.
:.3 Yh t`nongtrlggurrnat 6 Lb gurrnat pjssns thr ueh thn glrgult la ph t`nongtrlg nbbngt thna thn gurrnatls gjoonk ph`t`nongtrlg gurrnat.
:.7 U rm buagtl a 6[hn dlaldud nanrey rnqulrnk t` djmn ja nongtr`a brnn br`d thn dntjo ls gjoonkw`rm buagtl`a. Lt ls g`astjat b`r j dntjo jak kna`tnk cy`r U. Lt ls thn dlaldud b`r Gnslud. Lt lsrnojtlvnoy onss b`r jomjol dntjos.
U`rm buagtl as `b s`dn ph t`snasltlvn dntjos
Dntjo U`rm buagtl`a
(nv) Dntjo
U`rm buagtl`a(nR)
Gnslud :.< Gjoglud 7.3Y`tjsslud 3.3 G`ppnr ;.>
W`klud 3.7 Wlovnr ;.5Olthlud 3.> Yojtlaud >.2
[` pr`kugn ph`t` nongtrlg nbbngt `aoy dntjo jak oleht ls angnssjry cut b`r `csnrvlae lt, thn glrgult ls g`d-pontnk. Bleurn sh`ws ja jrrjaendnat usnk t` stuky thn ph`t`nongtrlg nbbngt.
: 3
JG
latnaslty
brnqunagy
Shn`stjt
gnoo, bnw v`ots
R
J
Hnrn thn pojtn (:) ls gjoonk ndlttnr `r gjth`kn jak `thnr pojtn (3) ls gjoonk g`oongt`r `r ja`kn.
:.; Wjturjtl`a gurrnat 6 Uhna joo thn ph t` nongtr`as ndlttnk cy gjth`kn rnjgh thn ja`kn thna gurrnatbo`wlae la thn glrgult jt thjt lastjat ls ma`wa js sjturjtnk gurrnat, thls ls thn djxldud vjoun `bph`t`nongtrlg gurrnat.
:.> Wt`pplaep`tnatljo6 Dlaldud djealtukn `b anejtlvn p`tnatljo `b ja`kn wlth rnspngt t` gjth`kn b`rwhlgh gurrnat ls znr` ls gjoonk st`pplae p`tnatljo. [hls ls jos` ma`wa js gut bb v`otjen. [hls v`otjenls laknpnaknat `b latnaslty.
:.2 Sntjrklae p`tnatljo 6 Anejtlvn p`tnatljo `b ja`kn wlth rnspngt t` gjth`kn whlgh ls onss thjast`pplae p`tnatljo ls gjoonk rntjrklae p`tnatljo.
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"djalshmudjrphyslgs.la" 3
3. @CWNSRJ[L@AW 6 DJKN C\ NLAW[NLA3.: J erjph cntwnna latnaslty `b oleht jak ph t`nongtrlg gurrnat ls b`uak
t` cn j strjleht olan js sh`wa la bleurn. Yh`t`nongtrlg gurrnat lsklrngtoy pr`p`rtl`ajo t` thn latnaslty `b laglknat rjkljtl`a. La thlsnxpnrldnat thnbrnqunagyjak rntjrklaep`tnatljojrn mnpt g`astjat.
Yh`t`gurrnat
Latnaslty `b oleht @
3.3 J erjph cntwnna ph`t`nongtrlg gurrnat jak p`tnatljo klbbrnagn cntwnna gjth`kn jak ja`kn ls b`uakjs sh`wa la bleurn.
sjturjtl`a gurrnat
3 :1
R RJ GRW
:
W3
W:
Y
La gjsn `b sjturjtl a gurrnat,rjtn `b ndlssl`a `b ph t`nongtr`as 4 rjtn `b bo`w `b ph t`nongtr`as ,hnrn, v
sst`pplae p`tnatljo jak lt ls j p`sltlvn qujatlty
Nongtr`as ndlttnk br`d surbjgn `b dntjo hjvn klbbnrnat nanrelns.Djxldud mlantlg nanrey `b ph`t`nongtr`a `a thn gjth`kn 4 nR
s
MNdjx
4 nRs
Uhnanvnr ph`t`nongtrlg nbbngt tjmns pojgn, nongtr as jrn nfngtnk`ut wlth mlantlg nanrelns rjaelae br`d
9 t` M.Ndjx l.n. 9MNGnRs[hn nanreyklstrlcutl`a `b ph t`nongtr`a ls sh`wa la bleurn.
A`.
`b
Yh`t`nongtr`as
Mlantlg nanrey nRW@
3.7 Lb latnaslty ls lagrnjsnk (mnnplae thn brnqunagy g`astjat) thna sjturjtl`a gurrnat ls lagrnjsnk cysjdn bjgt r cy whlgh latnaslty lagrnjsns. Wt`pplae p`tnatljo ls sjdn, s` djxldud vjoun `b mlantlgnanrey ls a`t nbbngtnk.
3.; Lb oleht `b klbbnrnat brnqunaglns ls usnk thna `ctjlank po ts jrn sh`wa la bleurn.
Lt ls gonjr br`d erjph, js lagrnjsns, st`pplae p`tnatljo lagrnjsns, lt dnjas djxldud vjoun `bmlantlg nanrey lagrnjsns.
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YH\WLGW
"djalshmudjrphyslgs.la" 7
3.> Erjphs cntwnna djxldud mlantlg nanrey `b nongtr`asnfngtnk br`d klbbnrnat dntjos jak brnqunagy `b oleht usnkjrn b`uak t` cn strjleht olans `b sjdn so`pn js sh`wa labluern
Erjph cntwnna Mdjx
jak
d:
th:
d3
th3
d7
th7
mdjxb`r dntjo's
d:, d
3, d
76 [hrnn klbbnrnat dntjos.
Lt ls gonjr br`d erjph thjt thnrn ls j dlaldud brnqunagy `b nongtr`djeantlg rjkljtl`a whlgh gjapr`kugn ph`t`nongtrlg nbbngt, whlgh ls gjoonk thrnsh`ok brnqunagy.
th
4 [hrnsh`ok brnqunagyB`r ph`t`nongtrlg nbbngt
th
b`r a` ph t`nongtrlg nbbngt ?th
Dlaldud brnqunagy b`r ph`t`nongtrlg nbbngt 4 th
dla
4th
[hrnsh`ok wjvnonaeth(th
)[hn djxldud wjvnonaeth `b rjkljtl`a whlgh gja pr`kugn ph`t`-nongtrlg nbbngt.
th
b`r ph t` nongtrlg nbbngt
Djxldud wjvnonaeth b`r ph`t nongtrlg nbbngt djx 4 th.A`w wrltlae nqujtl a `b strjleht olan br`d erjph.Un hjvn M
djx4 J+ C
Uhna 4 th
, Mdjx
4 9jak C 4 J
th
Hnagn ]Mdjx
4 J( th
)T
jak J 4 tja4 2.27 :97; F-s (br`d nxpnrldnatjo kjtj)ojtnr `a J wjs b`uak t` cn h.
3.2 Lt ls jos` `csnrvnk thjt ph t`nongtrlg nbbngt ls ja lastjatjan`us pr`gnss. Uhna oleht bjoos a surbjgnnongtr`as stjrt nfngtlae wlth`ut tjmlae jay tldn.
7. [HSNN DJF@S BNJ[^SNW @B [HN YH@[@NONG[SLG NBBNG[ GJAA@[ CN NXYOJLANKLA [NSDW @B [HN GOJWWLGJO UJRN [HN@S\ @B OLEH[.
Latnaslty 6 [hn nanrey gr`sslae pnr ualt jrnj pnrualt tldn pnrpnaklguojr t` thn klrngtl a `b pr`pj-ejtl`a ls gjoonk thn latnaslty `b j wjvn.
J x
g t
G`aslknr j gyolakrlgjo v`oudn wlth jrnj `b gr`ss-sngtl`a J jak onaeth gt jo`ae thn X-jxls. [hnnanreyg`atjlank la thls gyolaknr gr`ssns thnjrnjJ la tldnt js thn wjvn pr`pjejtns jt spnnk g.[hn nanrey g`atjlank.
^ 4 ujv(g.t)J
[hn latnaslty ls 4tJ
^
4 u
jvg.
La thn tnrds `b djxldud nongtrlg blnok,
43
:
9N
93 g.
Lb wn g`aslknr oleht js j wjvn thna thn latnaslty knpnaks up`a nongtrlg blnok.Lb wn tjmn w`rm buagtl`a U 4. J . t,
thna t 4J
U
s` b`r ph`t`nongtrlg nbbngt thnrn sh`uok cn tldn oje cngjusn thn dntjo hjs w`rm buagtl`a.Cut lt ls `csnrvnk thjt ph`t`nongtrlg nbbngt ls ja lastjatjan`us pr`gnss.Hnagn, oleht ls a`t `b wjvn ajturn.
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"djalshmudjrphyslgs.la" ;
7.: [hn latnaslty pr`cond 6 Ujvn thn`ry rnqulrns thjt thn `sgloojtlae nongtrlg blnok vngt`rN `b thn olehtwjvn lagrnjsns la jdpoltukn js thn latnaslty `b thn oleht cnjd ls lagrnjsnk. Wlagn thn b`rgn jppolnkt` thn nongtr`a ls nN, thls sueensts thjt thn mlantlg nanrey `b thn ph`t`nongtr`as sh`uok jos` la-grnjsnk js thn oleht cnjd ls djkn d`rn latnasn. H`wnvnr `csnrvjtl a sh`ws thjt djxldud mlantlgnanrey ls laknpnaknat `b thn oleht latnaslty.
7.3 [hn brnqunagy pr`cond 6Jgg`rklae t` thn wjvn thn`ry, thn ph`t`nongtrlg nbbngt sh`uok `ggur b`rjaybrnqunagy `b thn oleht, pr`vlknk `aoy thjt thn oleht ls latnasn na`ueh t` suppoy thn nanreyannknkt` nfngt thn ph`t`nongtr`as. H`wnvnr `csnrvjtl`as sh`ws thjt thnrn nxlsts b`r njgh surbjgn jghjrjgtnrstlg gut`bb brnqunagyth, b`r brnqunaglns onss thja th, thn ph`t`nongtrlg nbbngt k`ns a`t`ggur, a` djttnr h`w latnasn ls oleht cnjd.
7.7 [hn tldn knojy pr cond 6Lb thn nanrey jgqulrnk cy j ph`t`nongtr`a ls jcs`rcnk klrngtoy br`d thnwjvn laglknat `a thn dntjo pojtn, thn nbbngtlvn tjrent jrnj b r ja nongtr a la thn dntjo ls oldltnk jakpr`cjcoy a`t dugh d`rn thja thjt `b j glrgon `b kljdntnr r`uehoy nqujo t` thjt `b ja jt`d. La thngojsslgjo thn`ry, thn oleht nanreyls ualb rdoy klstrlcutnk `vnr thn wjvnbr`at. [hus, lb thn oleht ls bnnconna`ueh, thnrn sh`uok cn j dnjsurjcon tldn oje, cntwnna thn ldplaelae `b thn oleht `a thn surbjgnjak thn nfngtl`a `b thn ph`t`nongtr`a. Kurlae thls latnrvjo thn nongtr`a sh`uok cn jcs`rclae nanreybr`d thn cnjd uatlo lt hjkjgguduojtnk na`ueh t` nsgjpn. H`wnvnr, a` kntngtjcon tldn oje hjs nvnrcnna dnjsurnk.
A`w, qujatud thn`rys`ovns thnsn pr`conds la pr vlklae thn g`rrngt latnrprntjtl`a `b thn ph t`nong-
trlg nbbngt.
; YOJAGMW Z^JA[^D [HN@S\ 6[hn oleht nanrey br`d jay s`urgn ls jowjys ja latnerjo duotlpon `b j sdjoonr nanrey vjoun gjoonk qujatud boleht.hnagn nanrey Z 4 AN,whnrn N 4 h jak A (audcnr b ph t`as) 4 :,3,7,....Hnrn nanrey ls qujatlznk. hls thn qujatud `b nanrey, lt ls j pjgmnt `b nanrey gjoonk jsph`t`a.
N 4 h 4
hg
jak hg 4 :3;99 nR
>. NLAW[NLAW YH@[@A [HN@S\La : Nlastnla djkn j rndjrmjcon jssudptl`a jc`ut thn ajturn `b oleht= ajdnoy, thjt, uaknr s`dn glrgud-stjagns, lt cnhjvns js lb lts nanrey ls g`agnatrjtnk lat` o gjolznk cuakons, ojtnr gjoonk ph`t`as. [hn nanreyN `b j slaeon ph`t`a ls elvna cy
N 4 h,Lb wn jppoy Nlastnlas ph`t`a g`agnpt t` thn ph`t`nongtrlg nbbngt, wn gja wrltn
h4 U + Mdjx
, (nanreyg`asnrvjtl`a)
Nqujtl`a sjys thjt j slaeon ph`t`a gjrrlns ja nanrey hlat` thn surbjgn whnrn lt ls jcs`rcnk cy j slaeonnongtr`a. Yjrt `b thls nanreyU (gjoonk thn w rm buagtl a `b thn ndlttlae surbjgn) ls usnk la gjuslae thn nongtr`at` nsgjpn br`d thn dntjo surbjgn. [hn nxgnss nanrey (h U ) cng`dns thn nongtr`as mlantlg nanrey= lb thnnongtr`a k`ns a`t o`sn nanrey cy latnrajo g`oolsl`as js lt nsgjpns br`d thn dntjo, lt wloo stloo hjvn thls dughmlantlg nanrey jbtnr lt ndnrens. [hus M
djxrnprnsnats thn djxldud mlantlg nanrey thjt thn ph`t nongtr a gja
hjvn `utslkn thn surbjgn. [hnrn ls g`dpontn jernndnat `b thn ph`t a thn ry wlth nxpnrldnat.
A`w J 4 Ah A 4 hJ 4 a . `b ph`t`as laglknat pnr ualt tldn `a ja jrnj J whna oleht `b
latnaslty ls laglknat a`rdjooy.
Lb wn k`ucon thn oleht latnaslty, wn k`ucon thn audcnr `b ph`t`as jak thus k`ucon thn ph`t`nongtrlg gurrnat=wn k` a`t ghjaen thn nanrey `b thn laklvlkujo ph t`as `r thn ajturn`b thn laklvlkujo ph`t`nongtrlg pr gnssns.
[hn sng`ak `cfngtl`a (thn brnqunagy pr`cond) ls dnt lb Mdjx
nqujos znr , wn hjvnh
th4 U,
Uhlgh jssnrts thjt thn ph`t a hjs fust na`ueh nanrey t` nfngt thn ph`t`nongtr`as jak a`an nxtrj t` jppnjrjs mlantlg nanrey. Lbls rnkugnk cno`w
th, hwloo cn sdjoonr thja U jak thn laklvlkujo ph`t`as, a` djttnr
h`w djay `b thnd thnrn jrn (thjt ls, a` djttnr h`w latnasn thn looudlajtl`a), wloo a t hjvn na`ueh nanrey t`nfngt ph`t`nongtr`as.
[hn thlrk `cfngtl`a (thn tldn knojy pr`cond) b oo`ws br d thn ph`t`a thn`ry cngjusn thn rnqulrnk nanrey lssuppolnk la j g`agnatrjtnk cuakon. Lt ls a`t sprnjk ualb`rdoy `vnr thn cnjd gr`ss sngtl`a js la thn wjvnthn`ry.
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YH\WLGW
"djalshmudjrphyslgs.la" >
Hnagn Nlastnlas nqujtl a b`r ph`t`nongtrlg nbbngt ls elvna cy
h4 hth
+ Mdjx
Mdjx
4
hg
th
hg
Nx. : La ja nxpnrldnat `a ph t` nongtrlg ndlssl a, b`oo`wlae `csnrvjtl as wnrn djkn=(l) Ujvnonaeth `b thn laglknat oleht 4 :. v ot.Blak 6 (j) Mlantlg nanrey `b ph t`nongtr`as wlth djxldud spnnk.
(c) U`rm buagtl a jak(g) [hrnsh ok brnqunagy=W`o. (j) Wlagn v
s4 3.> R, M
djx4 nR
s s`, M
djx4 3.> nR
(c) Nanrey`b laglknat ph`t a
N 4 nR::97
Ud3
. [hn cnjd bjoos a rdjooy `a ja jrnj :9;
d3
`b j gonja dntjoolg surbjgn `b w rm buagtl a :.8 nR N
74
2999
:3;994 3.92 nR
jak N;4
5999
:3;994 :.55 nR
[hnrnb rn, oleht `b wjvnonaeths ;999 , ;899 jak 2999 gja `aoy ndlt ph`t`nongtr as. Audcnr `b ph t`nongtr`as ndlttnk pnr sng`ak 4 A`. `b ph t`as laglknat pnr sng`ak)
4:
::
N
J+
3
33
N
J+
7
77
N
J4J
73: N
:
N
:
N
:
4 :.:(
92.3
:
>8.3
:
:.7
:
4 :.:3 :9:3 Jas.
Nx. 7 J sdjoo p`tjsslud b`lo ls pojgnk (pnrpnaklguojr t` thn klrnglt`a `b laglknagn `b oleht) j klstjagn r (4 9.> d)br`d j p`lat oleht s`urgn wh`sn `utput p`wnr Y
9ls :.9U. Jssudlae wjvn ajturn `b oleht h`w o`ae w`uok lt
tjmn b`r thn b`lo t` s`jm upna`uehnanrey (4 :.8 nR) br`d thn cnjd t` nfngt ja nongtr`a0 Jssudn thjt thnnfngtnk ph t`nongtr a g`oongtnk lts nanreybr`d j glrguojr jrnj `b thn b`lo wh`sn rjklus nqujos thn rjklus `b jp`tjsslud jt`d (:.7 :9:9 d).
W`o. Lb thn s`urgn rjkljtns ualb`rdoy la joo klrngtl`as, thn latnaslty`b thn oleht jt j klstjagn r ls elvna cy
4 39
r;Y
4 3)d>.9(;U9.:
4 9.73 U/d3.
[hn tjrent jrnj J ls(:.7 :9:9 d)3 `r >.7 :939 d3, s` thjt thn rjtn jt whlgh nanrey bjoos `a thn tjrent lselvna cy
Y 4J 4 (9.73 U /d3) (>.7 :939 d3)
4 :.5 :939 F/s.Lb joo thls lag`dlae nanrey ls jcs`rcnk, thn tldn rnqulrnk t` jgguduojtn na`ueh nanrey b`r thn nongtr`a t`nsgjpn ls
t 4
s/F:95.:
nR8.:39
nR:
F:92.: :999, a` ph`t`nongtr`as jrn ndlttnk br`d thn surbjgn. Ulth ja uama`wa wjvnonaeth, st`pplae p`tnatljo ls 7 R.Blak thn uama`wa wjvnonaeth.
W`o. ^slae nqujtl a `b ph t`nongtrlg nbbngtM
djx4 N U (M
djx4 nR
s)
7 nR 4
:3;99
>999
:3;994
:3;99
3.;8 nR
`r 4 3323 Nx. > Looudlajtlae thn surbjgn `b j gnrtjla dntjo jotnrajtnoy wlth oleht `b wjvnonaeths
: 4 9.7> d jak
3
4 9.>; d, lt wjs b`uak thjt thn g`rrnsp`aklae djxldud vno gltlns `b ph t` nongtr as hjvn j rjtl` 4 3.Blak thn w`rm buagtl`a `b thjt dntjo.
W`o. ^slae nqujtl`a b`r tw` wjvnonaeths
Uhg
dv3
:
:
3:
....(l)
Uhg
dv3
:
3
33
....(ll)
Klvlklae Nq. (l) wlth Nq. (ll), wlth v:4 3v
3, wn hjvn ; 4
Uhg
Uhg
3
:
7U 4 ;
3
hg
:
hg4
>;99
:3;99;
7>99
:3;994 >.2; nR
U 47
2;.>nR 4:.88 nR Jas.
Nx. 2 J ph`t`gnoo ls `pnrjtlae la sjturjtl`a d`kn wlth j ph`t`gurrnat ;.8J whna j d`a`ghr`djtlg rjkljtl`a `bwjvnonaeth 7999 jak p`wnr : dU ls laglknat. Uhna ja`thnr d`a`ghr`djtlg rjkljtl a `b wjvnonaeth :2>9 jak p`wnr > dU ls laglknat, lt ls `csnrvnk thjt djxldud vno`glty`b ph`t`nongtr`a lagrnjsns t` tw` tldns.Jssudlae nbblglnagy `b ph`t`nongtr`a enanrjtl`a pnr laglknat t` cn sjdn b`r c`th thn gjsns, gjoguojtn,(j) thrnsh`ok wjvnonaeth b r thn gnoo(c) nbblglnagy `b ph`t`nongtr`a enanrjtl a. ](A . `b ph`t`nongtr`as ndlttnk pnr laglknat ph`t`a) :99T(g) sjturjtl a gurrnat la sng`ak gjsn
W`o. (j) M:4
7999
:3;99 U 4 ;.:7 U ...(l)
M34
:2>9
:3;99 U 4 5.>: U ....(ll)
Wlagn v3 4 3v: s`, M34 ;M: ...(llll)W ovlae jc`vn nqujtl`as, wn entU 4 7 nR
[hrnsh`ok wjvnoneth 94
7
:3;994 ;:77 Jas.
(c) Nanrey `b j ph`t a la blrst gjsn 47999
:3;994 ;.:7 nR
`r N:4 2.2 :9:< F
Sjtn `b laglknat ph t`as (audcnr `b ph t`as pnr sng`ak)
4 :
:
N
Y
4 : :9:>
pnr sng`ak
Audcnr`b nongtr`as nfngtnk 4 :
:7
:9>.:
:99.7
:99 4 3% Jas.
(g) Nanrey `b ph`t a la sng`ak gjsn
N34 :2>9
:3;99
4 5.>: nR 4 :3 :9
: pnr sng`ak
Audcnr `b nongtr`as ndlttnk pnr sng`ak 4:99
3 ;.5 :9:>
4
s:
) t + sla (8 :9:>
s:
)tT bjoos `a jdntjo surbjgnhjvlae w`rm buagtl`a 3.9 nR. Gjoguojtn thn djxldud mlantlg nanrey `b thn ph`t`nongtr as.W`o. [hn oleht g`atjlas tw` klbbnrnat brnqunaglns. [hn `an wlth ojrenr brnqunagy wloo gjusn ph`t`nongtr`as wlth
ojrenst mlantlg nanrey. [hls ojrenr brnqunagy ls
3
s:98
3
::>
[hn djxldud mlantlg nanrey `b thn ph`t`nongtr as lsM
djx4 h U
4 (;.:; :9:> nR-s)
:
:>
s3
:98 3.9 nR
4 >.35 nR 3.9 nR 4 7.35 nR.
2 B@SGN K^N [@ SJKLJ[L@A YH@[@ANjgh ph`t`a hjs j knblaltn nanrey jak j knblaltn olanjr d`dnatud. Joo ph`t`as `b oleht `b j pjrtlguojrwjvnonaeth hjvn thn sjdn nanrey N 4 hg/ jak thn sjdn djealtukn `bd`dnatud p 4 h/.
Uhna oleht `b latnaslty bjoos a j surbjgn, lt nxnrts b rgn a thjt surbjgn. Jssudn jcs`rptl`a jak rnbongtl`ag`nbblglnat `b surbjgn cn j jak r jak jssudlae a` trjasdlssl a.Jssudn oleht cnjd bjoos `a surbjgn `b surbjgn jrnj J pnrpnaklguojroy js sh`wala bleurn.
B`r gjoguojtlae thn b`rgn nxnrtnk cy cnjd `a surbjgn, wn g`aslknr b`oo`wlae gjsns.
Gjsn 6 (L)j 4 :, r 4 9
laltljo d`dnatud `b thn ph`t`a 4h
blajo d`dnatud b ph`t a 4 9
ghjaen la d`dnatud `b ph t`a 4h
(upwjrk)
Y 4h
nanrey laglknat pnr ualt tldn 4J
a . `b ph`t`as laglknat pnr ualt tldn 4
hJ 4
hgJ
t`tjo ghjaen la d`dnatud pnr ualt tldn 4 aY
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"djalshmudjrphyslgs.la" 8
4
h
hg
J
4g
J(upwjrk)
b`rgn `a ph`t`as 4 t`tjo ghjaen la d`dnatud pnr ualt tldn
4g
J(upwjrk)
b`rgn `a pojtn kun t` ph`t`as(B) 4 gJ
(k`wawjrk)
prnssurn 4J
B4
gJ
J4
g
Gjsn 6 (LL)whna r 4 :, j 4 9
latljo d`dnatud `b thn ph`t`a 4
h(k`wawjrk)
blajo d`dnatud b ph`t`a 4
h(upwjrk)
ghjaen la d`dnatud 4
h+
h4
h3
nanrey laglknat pnr ualt tldn 4 J
a`. `b ph`t`as laglknat pnr ualt tldn 4hg
J
t tjo ghjaen la d`dnatud pnr ualt tldn 4 a .Y
4hg
J.
h34
G
J3
b`rgn 4 t`tjo ghjaen la d`dnatud pnr ualt tldn
B 4g
J3(upwjrk `a ph t`as jak k`wawjrk `a thn pojtn)
prnssurn Y 4JB 4
gJJ3 4
g3
Gjsn 6 (LLL)Uhna ` ? r ? : j + r 4 :
ghjaen la d`dnatud `b ph`t`a whna lt ls rnbongtnk 4h3
(upwjrk)
ghjaen la d`dnatud `b ph`t`a whna lt ls jcs`rcnk 4h
(upwjrk)
a . `b ph`t`as laglknat pnr ualt tldn 4hg
J
A . `b ph`t as rnbongtnk pnr ualt tldn 4hg
J. r
A . `b ph`t a jcs rcnkpnr ualt tldn 4hg
J(: r)
b`rgn kun t` jcs rcnk ph`t`a (Bj) 4
hg
J(: r) .
h
4g
J(: r) (k wawjrk)
B`rgn kun t` rnbongtnk ph`t`a (Br) 4
hg
J.r
h3
4g
J3 (k`wawjrk)
t`tjo b`rgn 4 Bj+ Br (k`wawjrk)
4g
J(: r) +
g
Jr3
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"djalshmudjrphyslgs.la" 9)la( ....(v)
5.3 kn-Cr`eoln wjvnonaeth `b j ejs d onguon 6
Ont us g`aslknr j ejs d`onguon jt jcs`outn tndpnrjturn [. Mlantlg nanrey `b ejs d`onguon ls elvna cy
M.N. 43
7m[ = m 4 C`otzdja g`astjat
ejs d`onguon
4dm[7
h
Nx. :: Ja nongtr`a ls jggnonrjtnk cy j p`tnatljo klbbnrnagn `b >9 v ot. Blak thn kn-Cr eoln wjvnonaeth jss`gljtnk wlthlt.
W`o. B`r ja nongtr`a, kn-Cr`eoln wjvnonaeth ls elvna cy,
4
R
:>94
>9
:>94 7
4 :.57 Jas.
Nx. :3 Blak thn rjtl` `b Kn-Cr`eoln wjvnonaeth `b d`onguons `b hykr`enajak hnolud whlgh jrn jt tndpnrjturns 35Gjak :35G rnspngtlvnoy.
W`o. kn-Cr`eoln wjvnonaeth ls elvna cy
Hn
H3
4
33 HH
HnHn
[d
[d4
)35735(
)357:35(.
3
;
47
8
8. [H@DW@AW J[@DLG D@KNO 6F.F. [h`ds`a sueenstnk thjt jt`ds jrn fust p`sltlvnoy ghjren oudps `b djttnr wlth nongtr as ndcnkknk la
thnd olmn rjlslas la j brult gjmn. [h`ds`as d`kno gjoonk thn poud pukklae d`kno ls looustrjtnk la bleurn.
Nongtr`a
Y`sltlvnoy ghjrenk djttnr
[h`ds`a pojynk ja ldp`rtjat r`on la klsg`vnrlae thn nongtr`a, thr`ueh ejs klsghjren tucn cy klsg`vnrlae
gjth`kn rjys. Hls lknj wjs tjmna snrl`usoy.Cut thn rnjo jt`d turank `ut t` cn qultn klbbnrnat.
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"djalshmudjrphyslgs.la" :7
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"djalshmudjrphyslgs.la" :;
Wldlojroy, sucstltutlae vjouns `b n,9jak h wlth a 4 : la Nq. (v), wn ent
v:4 3.:< :92 d/s ....(vlll)
[hls ls thn ernjtnst p`sslcon spnnk `b thn nongtr`a la thn hykr`ena jt`d. Uhlgh ls jppr`xldjtnoynqujo t` g/:75 whnrn g ls thn spnnk `b oleht la vjguud.Nq. (v), la tnrds `b v
:gja cn wrlttna js,
va4
a
v: `r va
a
:
Nanrey onvnos 6 Mlantlg jak p`tnatljo nanrelns Majak ^ala ath `rclt jrn elvna cy
Ma4
3
:dv
a3 4 333
9
;
ha8
dn
jak ^a4
9;
:
a
3
r
n4
3339
;
ha;
dn
(jssudlae lablalty js j znr` p`tnatljo nanrey onvno)
[hn t`tjo nanrey Nals thn sud `b thn mlantlg jak p`tnatljo nanrelns.
s`, Na4 Ma+ ^a4 3339
;
ha8
dn
Wucstltutlae vjouns `b d, n,
9jak h wlth a 4 :, wn ent thn onjst nanrey `b thn jt`d la blrst `rclt, whlgh ls
:7.2 nR. Hnagn,N
:4 :7.2 nR ....(x)
jak Na4
3:
a
N4
3a
2.:7nR ....(xl)
Wucstltutlae a 4 3, 7, ;, ...., ntg., wn ent nanrelns `b jt`d la klbbnrnat `rclts.
N34 7.;9 nR, N
74 :.>: nR, .... N
4 9
:9.: Hykr ena Olmn Jt`ds[hn C`hr d`kno `b hykr`ena gja cn nxtnaknk t` hykr`ena olmn jt`ds, l.n., `an nongtr`a jt`ds, thnaugonjr ghjren ls +zn, whnrn z ls thn jt dlg audcnr, nqujo t` thn audcnr `b pr`t as la thn augonus.[hn nbbngt la thn prnvl us jajoysls ls t` rnpojgn n3 nvnrywhnrn cy zn3. [hus, thn nqujtl as b`r, r
a, v
a
jak Na
jrn jotnrnk js uaknr6
ra4 3
339
adzn
ha4
z
a3j
9 `r r
a
z
a3....(l)
whnrn j94 9.>3< (rjklus `b blrst `rclt ` b H)
va4
ah3
zn
9
3
4 a
zv
: `r v
a
a
z....(ll)
whnrn v:4 3.:< :92 d/s (spnnk `b nongtr a la blrst `rclt `b H)
Na4 333
9
;3
ha8ndz
4 3
3
az N
:`r N
a 3
3
az ....(lll)
whnrn N:4 :7.29 nR (nanrey `b jt`d la blrst `rclt b H)
:9.3 Knblajtl`as vjolk b`r slaeon nongtr a systnd(:) Er`uak stjtn 6O`wnst nanrey stjtn `b jay jt`d `r l`a ls gjoonk er`uak stjtn `b thn jt`d.
Er`uak stjtn nanrey `b H jt`d 4 :7.2 nREr`uak stjtn nanrey `b Hn+ L`a 4 >;.; nREr`uak stjtn nanrey `b Ol++ L`a 4 :33.; nR
(3) Nxgltnk Wtjtn 6Wtjtn `b jt`d `thnr thja thn er`uak stjtn jrn gjoonk lts nxgltnk stjtns.a 4 3 blrst nxgltnk stjtna 4 7 sng`ak nxgltnk stjtn
a 4 ; thlrk nxgltnk stjtna 4 a
9+ : a
9th nxgltnk stjtn
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"djalshmudjrphyslgs.la" :>
(7) L`alsjtl`ananrey ( N.)6 Dlaldud nanreyrnqulrnk t` d`vn ja nongtr a br`d er`uak stjtn t` a 4 ls gjoonk l`alsjtl a nanrey `b thn jt`d `r l`aL`alsjtl`a nanrey `b H jt`d 4 :7.2 nRL`alsjtl`a nanrey `b Hn+ L`a 4 >;.; nRL`alsjtl`a nanrey `b Ol++ L`a 4 :33.; nR
(;) L`alsjtl a p`tnatljo (L.Y.) 6 Y`tnatljo klbbnrnagn thr`ueh whlgh j brnn nongtr a dust cn jggnonrjtnkbr`d rnst sugh thjt lts mlantlg nanrey cng`dns nqujo t` l`alsjtl`a nanrey `b thn jt`d ls gjoonkl`alsjtl`a p`tnatljo `b thn jt`d.
L.Y `b H jt`d 4 :7.2 RL.Y. `b Hn+ L`a 4 >;.; R
(>) Nxgltjtl ananrey6 Nanrey rnqulrnk t` d`vn ja nongtr a br d er uak stjtn `b thn jt d t` jay `thnrnxltnk stjtn `b thn jt`d ls gjoonk nxgltjtl`a nanrey `b thjt stjtn.Nanrey la er`uak stjtn `b H jt`d 4 :7.2 nRNanrey la blrst nxgltnk stjtn `b H-jt`d 4 7.; nRst nxgltjtl`a nanrey 4 :9.3 nR.
(2) Nxgltjtl a Y`tnatljo6 Y tnatljo klbbnrnagn thr ueh whlgh ja nongtr`a dust cn jggnonrjtnk br`d rnsts` thjt lts mlantlg nanrey cng`dns nqujo t` nxgltjtl`a nanrey `b jay stjtn ls gjoonk nxgltjtl`ap`tnatljo `b thjt stjtn.st nxgltjtl`a nanrey 4 :9.3 nR.st nxgltjtl`a p`tnatljo 4 :9.3 R.
(5) Claklae nanrey `r Wnpnrjtl a nanrey 6Nanrey rnqulrnk t` d`vn ja nongtr`a br`d jay stjtn t` a4 ls gjoonk claklae nanrey `b thjt stjtn. `r nanrey rnonjsnk kurlae b`rdjtl`a `b ja H-olmn jt d/l`abr`d a 4t` s`dn pjrtlguojr a ls gjoonk claklae nanrey `b thjt stjtn.Claklae nanrey `b er`uak stjtn `b H-jt d 4 :7.2 nR
Nx. :7 Blrst nxgltjtl a p`tnatljo `b j hyp thntlgjo hykr`ena olmn jt`d ls :> v`ot. Blak thlrk nxgltjtl`a p tnatljo `b thnjt`d.
W`o. Ont nanrey `b er`uak stjtn 4 N9
N94 :7.2 V3 nR jak N
a4 3
9
a
N
a 4 3, N3
4;
N9
elvna;
N9 N94 :>
;
N7 9 4 :>
b r a 4 ;, N;4
:2
N9
thlrk nxlgltjtl`a nanrey 4:2
N9 N
9
4 :2
:>N
94
7
:>;
:2
:>
4;
5> nR
thlrk nxgltjtl`a p`tnatljo ls;
5>R
:9.7 Ndlssl a spngtrud `b hykr`ena jt`d 6
H-ejs
Wgrnna
Yrlsd
^aknr a`rdjo g`akltl`as thn slaeon nongtr`a la hykr`ena jt`d stjys la er`uak stjtn (a 4 :). Lt lsnxgltnk t` s`dn hlehnr nanrey stjtn whna lt jgqulrns s`dn nanrey br`d nxtnrajo s`urgn. Cut lthjrkjoy stjys thnrn b`r d`rn thja :98 sng`ak.
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"djalshmudjrphyslgs.la" :2
J ph`t`a g`rrnsp`aklae t` j pjrtlguojr spngtrud olan ls ndlttnk whna ja jt`d djmns j trjasltl`abr`d j stjtn la ja nxgltnk onvno t` j stjtn la j o`wnr nxgltnk onvno `r thn er`uak onvno.Ont a
lcn thn laltljo jak a
bthn blajo nanrey stjtn, thna knpnaklae `a thn blajo nanrey stjtn b`oo`wlae
snrlns jrn `csnrvnk la thn ndlssl`a spngtrud `b hykr`ena jt`d.@a Wgrnna 6J ph`t`erjph `b spngtrjo olans `b thn Oydna, Cjodnr, Yjsghna snrlns `b jt`dlg hykr`ena.
:
3
7
:
3
7
:3
Oydjasnrlns
Cjodnrsnrlns
Yjsghnasnrlns
Ujvnonaeth(lagrnjslae`rknr)
:, 3, 7..... rnprnsnats thn L, LL & LLL olan `b Oydna, Cjodnr, Yjsghna snrlns.
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"djalshmudjrphyslgs.la" :5
[hn hykr`ena spngtrud (s`dn snongtnk olans)
al (O`wnr Wtjtn a b(^ppnr Wtjtn) Uj vnonaeth (ad) Nanrey
L : 3 :3:.2 :9.3 nR
LL : 7 :93.2 :3.9< nR
LLL : ; > nR
LLL 3 > ;7;.: 3.82 nR
snrlns oldlt 3 (snrlns oldlt) 72;.2 7.;: nR
L 7 ; :85>.: 9.22 nR
LL 7 > :38:.8 9.;nR9.8>nR
:.>:nR
7.;9nR
:7.2nRa 4:
a 43
a 47
a 4;a 4>a 42a 45
B`r thn Oydna snrlns ab4 :, b`r Cjodnr snrlns a
b4 3 jak s` `a.
:9.; Ujvnonaeth `b Yh t`a Ndlttnk la Kn-nxgltjtl`aJgg`rklae t` C`hr whna ja jt`d djmns j trjasltl`a br`d hlehnr nanrey onvno t` j o`wnr onvno lt ndltsj ph`t`a wlth nanrey nqujo t` thn nanrey klbbnrnagn cntwnna thn laltljo jak blajo onvnos. Lb N
lls thn
laltljo nanrey `b thn jt`d cnb`rn sugh j trjasltl`a, Nbls lts blajo nanrey jbtnr thn trjasltl`a, jak thn
ph`t`as nanrey ls h4
hg , thna g`asnrvjtl`a `b nanrey elvns,
h4
hg4 N
l N
b (nanrey `b ndlttnk ph t`a) ....(l)
Cy :, F`hjaa Cjodnr, j Wwlss tnjghnr b`uak j b`rduoj thjt elvns thn wjvn onaeths `b thnsn olans.[hls ls a`w gjoonk thn Cjodnr snrlns. [hn Cjodnrs b`rduoj ls,
33 a
:
3
:S
:....(ll)
Hnrn, a 4 7, ;, > ...., ntg.
S 4 Sykcnre g`astjat 4 :.9
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"djalshmudjrphyslgs.la" :8
) `b thls snrlns ls `ctjlank. ^slae thn rnojtl`a, N 4
hgwn gja blak thn ph t`a nanrelns g`rrnsp`ak-
lae t` thn wjvnonaeth `b thn Cjodjr snrlns.
3333 a
Shg
3
Shg
a
:
3
:hgS
hgN
[hls b`rduoj sueensts thjt,
Na4 3
a
Shg, a 4 :, 3, 7..... ....(lll)
[hn wjvnonaeths g`rrnsp`aklae t` `thnr spngtrjo snrlns (Oydna, Yjsghna, (ntg.) gja cn rnprn-snatnk cy b`rduoj sldlojr t` Cjodnrs b rduoj.
Oydna Wnrlns 6
33 a
:
:
:S
:, a 4 3, 7, ;.....
Yjsghna Wnrlns 6
33 a
:
7
:S
:, a 4 ;, >, 2.....
Crjgmntt Wnrlns 6
33 a
:
;
:S
:, a 4 >, 2, 5.....
Ybuak Wnrlns 6
33
a
:
>
:S
:, a 4 2, 5, 8
[hnOydnasnrlns lslathn uotrjvl ont, jakthnYjsghna. Crjgmnttjak Ybuak snrlns jrnla thn labrjrnkrnel a.
Nx. :; Gjoguojtn (j) thn wjvnonaeth jak (c) thn brnqunagy `b thn H olan `b thn Cjodnr snrlns b`r hykr`ena.
W`o. (j) Holan `b Cjodnr snrlns g`rrnsp`aks t` thn trjasltl`a br`d a 4 ; t` a 4 3 onvno. [hn g`rrnsp`aklae
wjvnonaeth b`r H
olan ls,
335
;
:
3
:):992 :95
4 ;.< :95 d Jas.
(c) 4
g
4 5
8
:9 Blak thn ojrenst jak sh`rtnst wjvnonaeths la thn Oydna snrlns b`r hykr`ena. La whjt rnel`a `b thn nongtr`-djeantlg spngtrud k`ns njgh snrlns oln0
W`o. [hn trjasltl`a nqujtl`a b`r Oydna snrlns ls elvna cy,
33 a
:
):(
:S
:a 4 3, 7, ......
b`r ojrenst wjvnonaeth, a 4 3
;
:
:
::99; :95 d 4 :3:> Jas.[hn sh`rtnst wjvnonaeth g`rrnsp`aks t` a 4
:
:
::99
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YH\WLGW
"djalshmudjrphyslgs.la" : nR
7.98 nR
>.79 nR
:>.2 nR
(c) Blak thn sh rt wjvnonaeth oldlt b thnsnrlns tnrdlajtlae jt a 4 3
(g) Blak thn nxgltjtl a p tnatljo b r thn stjtna 4 7.
(k) Blak wjvn audcnr`b thn ph`t andlttnkb`r thn trjasltl`a a 4 7 t` a 4 :.
(n) Uhjt ls thn dlaldud nanrey thjt janongtr`a wloo hjvn jbtnr latnrjgtlae wlththls jt`d la thn er`uak stjtn lb thn laltljomlantlg nanrey `b thn nongtr`a ls(l) 2 nR (ll) :: nR
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YH\WLGW
"djalshmudjrphyslgs.la" 39
W`o. (j) L`alzjtl a p tnatljo 4 :>.2 R
(c) dla
47.>
:3;994 37;9
(g) N7:
4 7.98 ( :>.2) 4 :3.>3 nR[hnrnb`rn, nxgltjtl`a p`tnatljo b`r stjtn a 4 7 ls :3.>3 v`ot.
(k)7:
:
4 :3;99
N7:: 4
:3;99
>3.:3:
:.9: :95 d:
(n) (l) N3 N
:4 :9.7 nR 1 2 nR.
Hnagn nongtr`a gjaa`t nxgltn thn jt`ds. W`, Mdla
4 2 nR.(ll) N
3 N
:4 :9.7 nR ? :: nR.
Hnagn nongtr a gja nxgltn thn jt`ds. W`, Mdla
4 (:: :9.7) 4 9.5 nR.
Nx. 3: J sdjoo pjrtlgon `b djss d d`vns la sugh j wjy thjt thn p tnatljo nanrey ^ 4 jr3 whnrn j ls j g`astjat jakr ls thn klstjagn `b thn pjrtlgon br`d thn `rlela. Jssudlae C`hrs d`kno `b qujatlzjtl a `b jaeuojr d`dnatudjak glrguojr `rclts, blak thn rjklus `b ath joo`wnk rclt.
W`o. [hn b`rgn jt j klstjagn r ls,
B 4 kr
k^4 3jr
Wupp`sn r cn thn rjklus `b ath `rclt. [hn angnssjry gnatrlpntjo b`rgn ls pr`vlknk cy thn jc`vn b`rgn. [hus,
r
dv34 3jr
Burthnr, thn qujatlzjtl`a `b jaeuojr d`dnatud elvns,
dvr 43
ah
W`ovlae Nqs. (l) jak (ll) b`r r, wn ent
;/:
3
33
jd8
har
Jas.
Nx. 33 Ja ldjelajry pjrtlgon hjs j ghjren nqujo t` thjt `b ja nongtr`a jak djss :99 tldns thn djss `b thn nongtr`a.Lt d`vns la j glrguojr `rclt jr`uak j augonus `b ghjren + ;n. [jmn thn djss `b thn augonus t` cn lablaltn.Jssudlae thjt thn C`hrs d`kno ls jppolgjcon t` thn systnd.(j) Knrlvn jak nxprnssl`ab`r thn rjklus b ath C`hr `rclt.(c) Blak thn wjvnonaeth `b thn rjkljtl`a ndlttnk whna thn pjrtlgon fudps br`d b`urth `rclt t` thn sng`ak.
W`o. (j) Un hjvn 3a
3
9a
3p
r
zn
;
:
r
vd
.....(l)
[hn qujatlzjtl`a `b jaeuojr d`dnatud elvns,
dpvr
a4
3
ah......(ll)
W`ovlae Nqs. (l) jak (ll), wn ent
r 4 3p
933
ndz
ha
Wucstltutlae dp4 :99 d
whnrn d 4 djss `b nongtr`a jak z 4 ;
wn ent, r a4 3
933
dn;99
ha
Jas.
(c) Js wn ma`w,Nanrey `b hykr ena jt`d la er`uak stjtn 4 :7.29 nR
jak Na d
a
z3
3
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"djalshmudjrphyslgs.la" 3:
B r thn elvnapjrtlgon, N;4 3
3
);(
);()29.:7( :99 4 :729 nR
jak N34 3
3
)3(
);()29.:7( :99 4 >;;9 nR
KN 4 N; N
34 ;989 nR
(la ) 4 ;989:3;99
4 7.9 Jas.
Nx. 37 J pjrtlgon ma`wa js -dnjs`a, hjs j ghjren nqujo t` thjt `b ja nongtr a jak djss 398 tldns thn djss `b thnnongtr`a. Lt d`vns la j glrguojr `rclt jr`uak j augonus `b ghjren +7n. [jmn thn djss `b thn augonus t` cnlablaltn.Jssudlae thjt thn C`hrs d`kno ls jppolgjcon t` thls systnd, (j) knrlvn ja nxprnssl`a b`r thn rjklus`b thn ath C`hr `rclt, (c) blak thn vjoun `b a b`r whlgh thn rjklus `b thn `rclt ls jppr`xldjtnoythn sjdn js thjt`b thn blrst C`hr `rclt b`r j hykr`ena jt`d jak (g) blak thn wjvnonaeth `b thn rjkljtl`a ndlttnk whna thndns`a fudps br`d thn thlrk `rclt t` thn blrst `rclt.
W`o. (j) Un hjvn,
39
33
r;
Vn
r
dv
`r,d;
Vnrv
9
33
...(l)
[hn qujatlzjtl`a ruon ls vr 4d3
ah
[hn rjklus ls r 4rv
)vr(3
3
4 39
Vn
d;
4 39
33
dnV
ha
....(ll)
B`r thn elvna systnd, V 4 7 jak d 4 398 dn.
[hus 3n
933
nd23;
har
(c) Br`d (ll), thn rjklus `b thn blrst C`hr `rclt b`r thn hykr`ena jt`d ls
3n
93
hnd
hr
B`r r4 r
h, 3
n
933
nd23;
ha
4 3
n
93
nd
h
`r, a3
4 23;`r, a 4 3>(g) Br`d (l), thn mlantlg nanrey `b thn jt`d ls
3
dv34
r8
Vn
9
3
jak thn p`tnatljo nanrey ls r;
Vn
9
3
[hn t`tjo nanrey ls Na4
r8
Vn
9
3
^slae (ll), Na4 333
9
;3
ha8
dnV
4 333
9
;n
ha8
d398;>;>> pd.
Nx. 3; J ejs `b hykr`ena olmn jt`ds gja jcs`rc rjkljtl`as `b 28 nR. G`asnqunatoy, thn jt`ds ndlt rjkljtl`as `b`aoy thrnn klbbnrnat wjvnonaeth.Joo thn wjvnonaeths jrn nqujo `r sdjoonr thja thjt `b thn jcs`rcnk ph t`a.(j) Kntnrdlan thn laltljo stjtn `b thn ejs jt`ds.(c) Lknatlby thn ejs jt ds.(g) Blak thn dlaldud wjvnonaeth `b thn ndlttnk rjkljtl`as.(k) Blak thn l`alzjtl a nanrey jak thn rnspngtlvn wjvnonaeth b`r thn ejs jt`ds.
W`o. (j) 73
):a(a
a 4 7l.n., jbtnr nxgltjtl`a jt`d fudps t` sng`ak nxgltnk stjtn.Hnagn a
b4 7. W` a
lgja cn : `r 3
Lb al4 : thna nanrey ndlttnk ls nlthnr nqujo t`, ernjtnr thja `r onss thja thn nanrey jcs`rcnk.
Hnagn thn ndlttnk wjvnonaeth ls nlthnr nqujo t , onss thja `r ernjtnr thja thn jcs`rcnk wjvnonaeth.Hnagn a
l :.
Lb al4 3, thna N
nN
j. Hnagn
n
9
(c) N7 N
34 28 nR
(:7.2) (V3)
Ja nongtr`a ls `rcltlae la j glrguojr `rclt `b rjklus r uaknr thn labounagn `b j g`astjat djeantlg blnok `b strnaethC. Jssudlae thjt C`hrs p`stuojtn rnejrklae thn qujatlsjtl`a `b jaeuojr d`dnatud h`oks e``k b`r thlsnongtr`a, blak
(j) thn joo wnk vjouns b thn rjklus r b thn rclt.(c) thn mlantlg nanrey `b thn nongtr`a la rclt(g) [hn p`tnatljo nanrey b latnrjgtl`a cntwnna thn djeantlg d`dnat `b thn `rcltjo gurrnat kun t` thn
nongtr`a d`vlae la lts `rclt jak thn djeantlg blnok C.(k) [hn t tjo nanrey`b thn joo`wnk nanreyonvnos.
W`o. (j) rjklus `b glrguojr pjth
r 4Cn
dv....(l)
dvr 43
ah....(ll)
W`ovlae thnsn tw` nqujtl as, wn ent
r 4Cn3
ah
jak v 4 3d3
ahCn
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YH\WLGW
"djalshmudjrphyslgs.la" 37
(c) M 43
:dv3 4
d;
ahCn
Jas.
(g) D 4 l J 4
[
n(r3) 4
3
nvr
43
nCn3
ah
3d3
ahCn
4
d;
ahn
A`w p tnatljo nanrey ^ 4 D . C
4d;
ahnC
(k) N 4 + M 4d3
ahnC
::. NBBNG[ @B A^GON^W D@[L@A @A NANSE\ @B J[@DOnt c`th thn augonus `b djss D, ghjren Vn jak nongtr`a `b djss d, jakghjren n rnv`ovn jc`ut thnlr gnatrn `b djss (GD) wlth sjdn jaeuojrvno glty () cut klbbnrnat olanjr spnnks. Ont r
:
jak r3
cn thn klstjagn `b GDbr`d augonus jak nongtr a.[hnlrjaeuojr vno`glty sh`uok cn sjdn thna`aoy thnlr snpjrjtl`a wloo rndjla uaghjaenk la ja nanrey onvno.
dr3
GD
r:D
Ont r cn thn klstjagn cntwnna thn augonus jak thn nongtr`a. [hnaDr
:4 dr
3
r:+ r
34 r
r:4
dD
dr
jak r
34
dD
Dr
Gnatrlpntjo b`rgn t` thn nongtr`a ls pr`vlknk cy thn nongtr`stjtlg b`rgn. W`,
dr33 4
9;
:
3
3
r
Vn
`r d
dD
Dr3 4
9;
:
. 3
3
r
Vn
`r
dD
Ddr7 3 4
9
3
;
Vn
`r r73 49
3
;
n
whnrndD
Dd
4
D`dnat `b lanrtlj `b jt d jc`ut GD,
4 Dr:
3 + dr3
3 4
dD
Ddr3 4r3
Jgg`rklae t` C`hrs thn`ry,3
ah4
`r r3 43
ah
W ovlae jc vn nqujtl as b`r r, wn ent
r 4
Vn
ha3
339
jak r 4 (9.>3< )
d
V
a3
Burthnr nongtrlgjo p`tnatljo nanrey `b thn systnd,
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YH\WLGW
"djalshmudjrphyslgs.la" 3;
^ 4r;
Vn
9
3
^ 4 3339
;3
ha;
nV
jak mlantlg nanrey, M 43
:3 4
3
:r3 3 jak M 4
3
:v3
v-spnnk `b nongtr`a wlth rnspngt t` augonus. (v 4 r)
hnrn 3 4 79
3
r;
Vn
M 4 r8Vn
9
3
4 3339
;3
ha8
nV
[`tjo nanrey `b thn systnd Na4 M + ^
Na4 333
9
;
ha8
n
thls nxprnssl`a gja jos` cn wrlttna js
Na4 (:7.2 nR)
d
a
V3
3
[hn nxprnssl`a b`r Nawlth`ut g`aslknrlae thn d`tl`a `b pr`t`a ls N
a4 333
9
;
ha8
dn
, l.n., d ls rnpojgnk cy
whlon g`aslknrlae thn d`tl a `b augonus.
Nx. 32 J p`sltr`alud jt`d ls j systnd thjt g`aslsts `b j p`sltr`a jak ja nongtr`a thjt `rclt njgh thnr. G`dpjrnthn wjvnonaeth `b thn spngtrjo olans `b p`sltr`alud wlth th`sn `b rklajry hykr`ena.
W`o. Hnrn thn tw` pjrtlgon hjvn thn sjdn djss d, s` thn rnkugnk djss ls
4Dd
dD
4
d3
d34
3
d
whnrn d ls thn nongtr`a djss. Un ma`w thjt Nad
3:
dN
'N
a
a
nanrey `b njgh onvno ls hjovnk. [hnlr klbbnrnagn wloo jos` cn hjovnk.
Hnagn a
4 3a
:3. J[@DLG G@OOLWL@ALa sugh g`oolsl`as jssudn thjt thn o`ss la thn mlantlg nanrey `b systnd ls p`sslcon `aoy lb lt gja nxgltn `rl`alsn.
Nx. 35 H jt`d jt rnstla er`uak stjtnjak brnn t` d`vn
anutr`a
M, v
hnjk `a g`oolsl`a
Uhjt wloo cn thn typn `b g`oolsl`a, lb M 4 :;nR, 39.; nR, 33 nR, 3;.:8 nR(nojstlg/lanojstlg/pnrngtoy lanojstlg)
W`o. O`ss la nanrey(N) kurlae thn g oolsl`a wloo cn usnk t` nxgltn thn jt`d r nongtr`a br`d an onvno t` ja`thnr.Jgg`rklae t` qujatud Dnghjalgs, b`r hykr`ena jt`d.
N 4 {9, :9.3 nR, :3.9< nR, ........., :7.2 nR)Jgg`rklae t` Anwt`al`a dnghjalgs
dlaldud o`ss 4 9. (nojstlg g oosl a)
b`r djxldud o`ss g`oolsl`a wloo cn pnrbngtoy lanojstlg d d vblb anutr`a g`oolkns pnrbngtoy lanojstlgjooythna, Jppoylae d`dnatud g`asnrvjtl`a
d94 3d
b
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YH\WLGW
"djalshmudjrphyslgs.la" 3>
3
vv 9b
blajo M.N. 43
: 3d
;
39
4
3
d3
: 39
4
3
M
djxldud o`ss 43
M
Jgg`rklae t` gojsslgjo dnghjalgs (N) 4 ]9,3
MT
(j) Lb M 4 :; nR, Jgg rklae t` qujatud dnghjalgs(N) 4 {9, :9.3nR, :3.9< nR}Jgg`rklae t` gojsslgjo dnghjalgsN 4 ]9, 5 nRTo`ss 4 9, hnagn lt ls nojstlg g`oolsl`a spnnk `b pjrtlgon ghjaens.
(c) Lb M 4 39.; nRJgg`rklae t` gojsslgjo dnghjalgs
o`ss 4 ]9, :9.3 nRTJgg`rklae t` qujatud dnghjalgs
o`ss 4 {9, :9.3nR, :3.9.(
3
: 39 4 )dv3
:.(
>
: 39 4 >
M
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"djalshmudjrphyslgs.la" 32
djxldud o`ss 4 M >
M4
>
M;
s` o`ss wloo cn
>
M;,9 ....(3)
B`r lanojstlg g`oolsl`a thnrn sh`uok cn jt onjst `an g`dd`a vjoun `thnr thja znr` la snt (:) jak (3)
>
M;
1 ;9.8 nRM 1 >: nR
dlaldud vjoun `b M 4 >: nR.
Nx. 3< J d`vlae hykr`ena jt`d djmns j hnjk `a g`oolsl`a wlth j stjtl`ajry hykr`ena jt`d. Cnb`rn g`oolsl`a c`thjt`ds jrn la er`uak stjtn jak jbtnr g`oolsl`a thny d`vn t`enthnr. Uhjt ls thn dlaldud vjoun `b thn mlantlgnanrey `b thn d`vlae hykr`ena jt`d, sugh thjt `an `b thn jt`ds rnjghns `an `b thn nxgltjtl`a stjtn.
W`o. Ont M cn thn mlantlg nanrey `b thn d`vlae hykr`ena jt`d jak M, thn mlantlg nanrey `b g`dclank djss jbtnrg`oolsl`a.Br`d g`asnrvjtl`a`b olanjr d`dnatud,
N 4 :9.3 nR
a 4 3
a 4 :
p 4 p `r Md3 4 )d3('M3
r M 4 3M ....(l)Br`d g`asnrvjtl a `b nanrey, M 4 M +N ....(ll)
W`ovlae Nqs. (l) jak (ll), wn ent N 43
M
A`w dlaldud vjoun bN b`r hykr`ena jt`d ls :9.3 nR.`r N :9.3 nR
3
M:9.3
M39.; nR[hnrnb rn, thn dlaldud mlantlg nanrey`b d`vlae hykr`ena ls 39.; nR Jas.
Nx. 79 J anutr`a d`vlae wlth spnnk v djmns j hnjk-`a g oolsl`a wlth j hykr`ena jt d la er`uak stjtn mnpt jt rnst.Blak thn dlaldud mlantlg nanrey`b thn anutr`a b`r whlgh lanojstlg (g`dpontnoy `r pjrtljooy) g`oolsl a djy tjmnpojgn. [hn djss `b anutr`a 4 djss `b hykr`ena 4 :.25 :935 me.
W`o. Wupp`sn thn anutr`a jak thn hykr`ena jt d d`vn jt spnnk v:
jakv3
jbtnr thn g`oolsl`a. [hn g`oolsl`a wloo cnlanojstlg lb j pjrt `b thn mlantlg nanrey ls usnk t` nxgltn thn jt`d. Wupp`sn ja nanrey N ls usnk la thls wjy.^slae g`asnrvjtl`a `b olanjr d`dnatud jak nanrey.
dv4dv:
+ dv3
....(l)
jak3
:dv3 4
3
:dv
:3 +
3
:dv
33 +N ....(ll)
Br`d (l), v3 4 v:
3 + v3
3 + 3v:v
3,
Br`d (ll), v3 4 v:
3 + v3
3 +d
N3
[hus, 3v:v
34
d
N3
Hnagn, (v: v
3)3 ;v
:v
34 v3
d
N;
Js v: v
3dust cn rnjo, v3
d
N;9
`r,3
:dv3 1 3N.
[hn dlaldud nanreythjt gja cn jcs`rcnk cy thn hykr`ena jt d la er uak stjtn t` e` la ja nxgltnk stjtn ls:9.3 nR. [hus, thn dlaldud mlantlg nanrey `b thn anutr`a annknk b`r ja lanojstlg g`oolsl`a ls
nR;.39nR3.:93dv3: 3
dla
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"djalshmudjrphyslgs.la" 35
Nx. 7: H`w djay hnjk-`a, nojstlg g`oolsl`as dust j anutr a hjvn wlth knutnrlud augonus t` rnkugn lts nanreybr`d: DnR t` 9.93> nR.
W`o. Ont djss b anutr a 4 d jak djss b knutnrlud 4 3dlaltljo mlantlg nanrey `b anutr`a 4 M
9
Ont jbtnr blrst g`oolsl`a mlantlg nanrey `b anutr`a jak knutnrlud cn M:jak M
3.
^slae [email protected]. jo`ae klrngtl`a `b d`tl`a
9dM3 4 :dM3 + 3dM;
vno glty `b snpnrjtl`a 4 vno glty `b jppr`jgh
d3
dM; 3 d
dM3 : 4d
dM3 9
W ovlae nqujlt a (l) jak (ll) wn ent
M:4
39 4 :97 nR 4 :97 nR.
[hus, nR:9
h 7
4 nR:9
)s/d:97()snR:9:;.;(
7
8:>
4 ad3;.:
nR:9
adnR:3;3
7
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YH\WLGW
"djalshmudjrphyslgs.la" 79
3. GhjrjgtrlstlgX-rjys[hn shjrp pnjms `ctjlank la erjph jrn ma`wa jsghjrjgtnrlstlg x-rjys cngjusn thny jrn ghjrjgtnrlstlg `btjrent djtnrljo.
:,
3,
7,
;, ........ 4 ghjrngtnrlstlg wjvnonaeth `b
djtnrljo hjvlae jt`dlg audcnr V jrn gjoonk ghjrjgtnrls-tlg x-rjys jak thn spngtrud `ctjlank ls gjoonkghjrjgtnrlstlg spngtrud. Lb tjrent `b jt dlg audcnr V ls
usnk thna pnjms jrn shlbtnk.
R, V
: 3
7
; dla
Ghjrjgtnrlstlg x-rjy ndlssl`a `ggurs whna ja nanrentlgnongtr`a g`oolkns wlth tjrent jak rnd`vn ja laanr shnoonongtr a br`d jt`d, thnvjgjagygrnjtnk la thn shnoo ls bloonkwhna ja nongtr`a br`d hlehnr onvno kr`ps lat` lt.Wupp`sn vjgjagy grnjtnk la laanrd`st M-shnoo ls bloonk cyja nongtr`a kr`plae br`d anxt hlehnr onvno O-shnoo thna M
ghjrjgtnrlstlg x-rjyls `ctjlank. Lb vjggjayla M-shnoo ls bloonkcy ja nongtr a br`d D-shnoo, M
olan ls pr`kugnk jak s` `a
sldlojroy O, O
,.....D
, D
olans jrn pr`kugnk.
dla : 3 7 ;
R, V' ? V
R, V
: 3 7 ;
M D D
A
M
M
O O O
a4>a4;
a47
a43
a4:
x-rjys
O
M
DA
@
Nx. 7; Blak whlgh ls Mjak M
o : o 3
:
3
W`o. N 4
hg, 4
N
hg
slagn nanrey klbbnrnagn `b M
ls onss thja M
Nm
?Nm
m
? m
: ls Mjak 3 ls M
Nx. 7>
: 3
:3
Blak whlgh ls Mjak O
W`o NM
1 NO
: ls Mjak 3 ls O
:;. D@WNON\W OJU 6D`snony dnjsurnk thn brnqunaglns `b ghjrjgtnrlstlg x-rjys b`r j ojren audcnr `b nondnats jak po`ttnk thnsqjurn r` t `b brnqunagy jejlast p`sltl a audcnr la pnrl`klg tjcon. Hn klsg`vnrnk thjt po t ls vnry go`snk t`j strjleht olan a`t pjsslae thr`ueh `rlela.
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YH\WLGW
"djalshmudjrphyslgs.la" 7:
:, : : :', ' ', ' ''
3, 3 3 3', '', '' '
V
V: o : o 3
V3 o :' o 3'
V7 o :" o 3''
V; o :"' o 3'''
Ujvnonaeth `b ghjrjgtrlstlg wjvnonaeths.
D`snonys `csnrvjtl`as gja cn djthndjtlgjooy nxprnssnk js
)cV(j
j jak c jrn p`sltlvn g`astjats b`r `an typn `b x-rjys & b`r joo nondnats (laknpnaknat `b V).D`snonys Ojw gja cn knrlvnk `a thn cjsls `b C`hrs thn`ry `b jt`d, brnqunagy `b x-rjys ls elvna cy
4
33
3: a
:
a
:GS . (V c)
cy uslae thn b`rduoj
:4 S z3
33
3: a
:
a
:wlth d`klblgjtl`a b`r duotl nongtr`a systnd.
c ma`wa js sgrnnalae g`astjat `r shlnoklae nbbngt, jak (V c) ls nbbngtlvn augonjr ghjren.b r M
olan
a: 4 :, a
34 3
4;
SG7(V c)
4 j(V c)
Hnrn j 4;
SG7, ]c 4 : b`r M
olansT
Nx. 72
: 3
M
M
V:
V3
Blak la V:
jak V3
whlgh `an ls ernjtnr.
W`o.
33
3: a
:
a
:gS . (V c)
Lb V ls ernjtnr thnawloo cn ernjtnr,wloo cn onss
:
? 3 V: 1 V3.
Nx. 75 J g`cjot tjrent ls c`dcjrknk wlth nongtr`as jak thn wjvnonaeth `b lts ghjrjgtnrlstlg spngtrud jrn dnjsurnk.J sng`ak, bjlatnr, ghjrjgtnrlstlg spngtrud ls jos` b`uak cngjusn `b ja ldpurlty la thn tjrent. [hn wjvnonaeth`b thn M
olans jrn :58.< pd (g`cjot) jak :;7.> pd (ldpurlty). Uhjt ls thn ldpurlty0
W`o. ^slae D`snonys ojw jak puttlae g/b`r(jak jssudlae c 4 :), wn `ctjla
jjVg
9
9
gg
jak jjVg
x
x
Klvlklae ylnoks
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YH\WLGW
"djalshmudjrphyslgs.la" 73
:V
:V
9
9
g
x
x
g
Wucstltutlae elvns us
pd>.:;7
pd pd
W`o. D`snonys nqujtl`a ls
)cV(jv
[hus, )cV(jg
::
....(l)
jak )cV(jg
33
....(ll)
Br`d (l) jak (ll) )VV(j::
g 3:3:
`r, j 4
3:3:
::
)VV(
g
435;3
)s/d:97( 3/:8
3/::33/::3 )d:9>.:58(
:
)d:95:(
:
4 >.9 :95 (Hz):/3
Klvlklae (l) cy (ll),
cV
cV
3
:
:
3
`r, c35
c;3
5:
>.:58
`r, c 4 :.75
Yr`cond :. Blak thn d`dnatud b j :3.9 DnR ph`t`a.
W`outl`a 6 p 4g
N4 :3 DnR/g.
Yr`cond 3. D`a`ghr`djtlg oleht `b wjvnonaeth 7999 ls laglknat a rajooy `a j surbjgn `b jrnj ; gd3. Lb thnlatnaslty `b thn oleht ls :> :93 U/d3, kntnrdlan thn rjtn jt whlgh ph`t`as strlmn thn surbjgn.
W`outl`a 6 Sjtn jt whlgh ph`t`as strlmn thn surbjgn
4
/hg
J
ph`t`a/F:927.2
s/F:92:
4 :9:7 ph`t`a/s.
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"djalshmudjrphyslgs.la" 77
Yr`cond 7. [hn mlantlg nanrelns `b ph`t nongtr as rjaen br`d znr` t` ;.9 :9:< F whna oleht `b wjvnonaeth 7999 bjoos `a j surbjgn. Uhjt ls thn st`pplae p`tnatljo b`r thls oleht 0
W`outl`a 6 Mdjx
4 ;.9 :9:< F F:92.:
nR:: nR..
[hna, br`d nRs4 M
djx, R
s4 3.> R.
Yr`cond ;. Uhjt ls thn thrnsh`ok wjvnonaeth b`r thn djtnrljo la jc`vn pr`cond 0
W`outl`a 6 3.> nR 4 th
77 .nR:9;.:3
7999
.nR:9;.:3
W`ovlae, th
4 5>. Blak thn kn Cr`eoln wjvnonaeth b j 9.9: me pnoont hjvlae j vno`glty `b :9 d/s.
W`outl`a 6 4 h/p 4s/d:9me9:.9
s.F:927.2 7;
4 2.27 :937 .
Yr`cond 2. Kntnrdlan thn jggnonrjtlae p`tnatljo angnssjry t` elvn ja nongtr a j kn Cr`eoln wjvnonaeth b : ,whlgh ls thn slzn `b thn latnrjt`dlg spjglae `b jt`ds la j grystjo.
W`outl`a 6 R 4 39
3
nd3
h
4 :>: R..
Yr`cond 5. Kntnrdlan thn wjvnonaeth `b thn sng`ak olan `b thn Yjsghna snrlns b`r hykr`ena.
W`outl a .:
4 (:.9
:
7
:`r 4 :3,839 .
Yr`cond 8. H`w djay klbbnrnat ph`t`as gja cn ndlttnk cy hykr`ena jt`ds thjt uaknre` trjasltl`as t` thner`uak stjtn br`d thn a 4 > stjtn 0
W`outl`a 6 A` `b p`sslcon trjasltl`a br`d a 4 > jrn 3>G 4:9
Jas. :9 ph`t`as.
Yr`cond
7/21/2019 Modern Physics - 1 Theory_E
34/34
YH\WLGW
4 2.8 3a
:nR
(l) N:4 2.8 nv
N34 2.8 33
:nR 4 :.59 nR
N74 2.8 37
:nR 4 9.52 nR
(ll) N (73) 4 N7 N
34 9.52 ( :.59) nR
4 9.:.9 nv
>
m;4 >: m 4 27.5> nR
Yr`cond :3. J [R tucn `pnrjtns wlth j 39 mR jggnonrjtlae p tnatljo. Uhjtjrn thn djxldudnanreyXrjys br`dthn [R snt 0
W`outl`a 6 [hn nongtr as la thn [R tucn hjvn ja nanrey`b 39 mnR, jak lb thnsn nongtr as jrn cr ueht t` rnst cy
j g`oolsl`a la whlgh `an Xrjy ph`t`a ls ndlttnk, thn ph`t`a nanrey ls 39 mnR.
Yr`cond :7. La thn D`snony rnojtl`a, )cV(jv whlgh wloo hjvn thn ernjtnr vjoun b`r thn g`astjat j b`r M `r
M
trjasltl`a 0W`outl`a 6 J ls ojrenr b`r thn M
trjasltl`as thja b`r thn M
trjasltl`as.