1. PALLTWEAB r{rfilA7'rgfU$ Aru4&l 8,rilfd&, BEI,I?AYd
dao k<tto& oltu, otda.la
J= olo
=lL= -2 e-3/q
L
4 CZ,* $ t r
#,.s(h Y, ) * n-stq" C-; q r,rff'"
n#,-E r*y' tfstnL+g cost
- -4 . _"/4L UEi ^ t4 - 5laL-
=.
aD'- a'2. 6eslL-;.ffi, e Jrn uEr
,_
+,n-r,^
!,, $,
,1 '3lqb rl?l a -
+ ieA
J'-' -"o,
ff+ 4 7, stn +- + Z cosL
= -llr"-utooro, g LoZr-ila'"r" ry r-*u,e-'/ot*rn t
- ry n -'lo"",n
S + ^lt smL +2[) cost
= -Y e-bl4t.o' $t - 2)--'t
e-dot r,r, S a +i sm'+ lcos+
=2"-z/aLr6s Su*e-zt{tr,n gt +!stn b +f casu
ilnUut< Vbesar CL-e)
ma,Ka nt(at
n - U4b
7u" cosEu-4r->la+A ;Ere 'stn
Svhgga orut I --: stn t 1 z Cos +
UT.
Toq
Ct V
"sar)
.
,{4?Erdrtru*
2. "a[,r?uffAffi
ilAla&r,(mgil764arsAArA#6g4r7utrq
!= d.a
a
= - b. ec-314L Ccr ros q t*+ e2- srn
4 : un L-s/a)L
c-F c,st, fl t4
+ E (z co.r
Y il* i r, n b- t cos',
Xco) =o c_>l"it
6= -zl4 e C ct cos fl y*.crstn uEi d+ec'3t4)LC-ZJcrsto
q b+$ czcos $r)+€stnt-f cost
T co)=o
J=-sto eL-''o'u C", cos S-o + Cz stn
*.o) + e 6'e/a)o
- V ",srn ry o*ryCeco,y
ry o)+6r,no-_ecoso
o= -* C., .u" o+ czstno) + t C- ry Ct sro O+ ry Cz coso)
1?.o^| r
e; -glq Cer.l{ 1z.o)t
e-- -] cz"t+ c- Y
O=6- z-4
A ------
o--E cz-a.A ,b
YSc, o+g cz-t)-;
i o+g c,)-Z
Utt
-/a
l--- G
Cz =a t 4
b rzt
hdr',n_tlq)Lrz
0=9 " ( -3
=!vla
tIEr t1
cos Vb * ffi, stn E' r4
vvt
r2T3Jtn{2- 7 cort-
3. "AilZyKArWe*tWFrrgmEff764$/B,rtr4(..{BEErZAZrd
htt2: -b J
2.2
?engelesa(ao umu rD
&h= C,e
C-3/4Y
cos tfTi
2
- 219 -AA +sb >4
->A+bB:4 -."C>)
{ Me+.d"e elrmtnast
-3.4 *'blb = 4
5A t>b =O _
-
-bA = t)
A '-- 1L
b
-
.5
Qangelesatan rchuJuc :
&P = - E ."t u tt stn
pznV olesa.la"o Unl u rh i
G = oh +,9ro
= c1e -' ."ro, E
7- zlilL 4
= e (Acos
,f-
= -b ! l=l = -b ) tlJi-;
4
homog en ,
g' -+ Cz e.'-'Wrrn +
Fun 9J, Q7rcoba.aP ,
6=A carts+ BstnL
0l=-Aglnbt Bcost
o'r. -h cosa - esin E
}enga,n mensubtr+ttuJr kao ke Qersatmaq.o Cl, dteeroleh,
zC-Acos& -Bstnt)*e C-A.9(nt tBcost)+S CAcos b + Bstn L) = 4Jtn t
zAcost*:EJrnt- bA stn$ tae cosb )E*..os b + BBstn b--4.f aht
- 2 *i 3g +5*>O
bA+3ta--O.--c4)
+ $,1ggode 6abJt t$(I81
>/+ t ab=O
b'(-3 + ze--ozr
-2 +>b= o
bb' 2
b= 2
Z
btcr€c-'/o)*rrrt -e corb 4$stot
5' r* czrtn $, )- Zr*Et1srn!
UnkUk rngnen€$t<ao Cr dofi Cz Ktea eunaka.n Syarab aD al 6 Co)
= @ da,o I. cO) =O
r -3la ).n
?="
1 -t1' " ccr co$
4 -"r czsrn Y il -f roto+; stno.
Q= C1- ?,
Ct= Z
b
-t.O
*I4IW{/tIT{A
4. P4[L?%ffiffi il,ilWF,f&tU$ ff8648/ 6,rtr4&,1 BEEl?Alrq
d.ao
a--da
w
= -?e-at C- |, ,* b -E"nn t ) + e- ""C?slnr - #r*Q+ * e"t
=
I o''* 2u -z*. L -zL tz -ot- 7re cos t +*e-='rrnt -f
fie-=l,n E -X e-22u u+* e4E
= - 8- o-'*.o, t" + *_n-r*stn { + * n
o,
Z't " Tz'
= I ^-zV=
ue-h- C- A cos E * 26 srn +) + * "o,
o.(aalah arus I cu) d,alaftt rzzfiglr.alao ?Vc SePerUt Qanbat'
.,lr.bard a,b t n,' . (bagoLtm ao a ?en'l a ktroya taa L E beSar t
:4oStDtUd€
C =oto7
DtK : ?. bo ottm i
L = Ao rtenrU;
L-' oto' Pa"adi
E *- ao -ftn tr W+>
O* : * can tah a,rus T Ce)
r baga(mofla lea{@kunva Saa€ L b€sa(- ?
Jawab t
{-[u.,t u- Ettchot$ I
zOd'r+ 3oor + '/o,or0; 40 ctn L
7-Otttl6'+ Dd = 4rtn E -' Ct)
?Dv domogen :
zO't+)O-t+ba=o
'lerSarnaan ban Ltt "
z(z + Dr-t 5;o
il418rutflru
5. -
P40lruKnf&r{4ilA7,*4m8ilEdg0l6,fAr4ffi aEEfi AArq
9engan vlgnJub.f+tLuJtsao k'e versamaoLo cl tP€rdeh:
6 Aeat + 4 c4 A e%) > CAeau) = 2 eAL
l6 AeAb+ tG Aeo" t D AeqL' z€4L
Z1 A >2
A-2-fr-
-b7
)adi,&p-- #rot
Qon'ta lesatan rJmun : '
G -- Ch +eP
= Ct€* 2 lcos
t * Cz e-' tnt t *r "
ot .
= e-2t Crr Cos t * Cz stn t) n
? nOt
unguk menecrt uka.tr Ct do$t C z <-tba Qunakan saa'ra? a)Dat
(} to) =-o do.n f,co)=o
& Co) =o
6, . c. Q-'rco, v + cze'?
tsto
e + Zz eot
O, Ct€ -e ocos O + Cze-2 'ostn6 + 9- e+'o
= Aeo. l+
= Cr' l't +
__ c, + *t
Ct = -9.>7
A= do
*
=-Oe-'b CCr cos a lCzsrnd *e->L C-Csrn E*Czcost) e4L+-g
3'7
a
Cteo. o + * n"
cz-. I . o + |-r. t
{r ICo)=O
tl- ae'arCcr.ost*cz grr t)-(e-'E Gc's(0'* cacos E) +*r"or
e: -ee-"-o Ccr cosO+ Castno] te-a'oGcr.crno t czcoso) + fl e4'o
:_a-r Cct . r *Cz.o)t t (_ct .ol cz_r)+ ], .t
:-a C-+)+c,+*? z
=1 , I_;_ +; + Cz
z7 "-7
fo- 12ve €
'b7
)adt, & -- e-'L C-
+ Cos $ -
E srn k) { 2-
37
e4"
6. -
P00lZHtrnf&il,f alUF,fgm?ffEdg9lB"rArq(.,f BEtrrf AZVi
O3. agn+. jrcaQan YnUa n arur I Eebaqa w atc+a+
doiarn s€buab ray:rqkatlao ?Lc rJtka ?>zto ohvnr V= lo hpnrv i c >oroz
FaraA da,o v = aoe4bvolb r olanqoLo svaraL a(Dat :I =o, 0=o ati
V--o ?a Aa saaL s a.t'lac )I+UEU-P' 1€n+uk atc,ab 1,tua t aru.r I
Saa* + besa" -
gtx: (=4O o6m;
L : to hehr9;
C : O toz farad ;
v -- ao€ Ab
,,)olb )
eengao {'Ya,ra.L a-Dat '.
a .O i 6}=0 altu-O
?a Aa saot* saq;fa* cltbq+uP
olb, Tgntul.ao kuatg T sebagat (uLn6J vcatk*u t dart mua+oto o P
)avcab'.
Htrkurn ktrchoFt'
Lo'r{ee'+*a r Ecv)
loo
(
+ Aoot + r / otoz. o -- ao e't{
o"-+ 4or+ Ee: eoe4l... ct)
?oL Homo $Qn:
c) 'f + 4&t + Bd;o
?ers om aa$ bar+u 1
11.z t4F + B--O
I^t12 : -trt $z- 4ac
= -zli
z.l
- 4 ! l=a-
--2
-4*- zi
2
=-zLi
V enlelesotl an umurn
(}h = ct?'" Crt a 'Y
Fun 6 J, (erabaan '.
A = AeAL
.($'= zlAe{t
O,' = lb Ag4b
bomo gon :
-Zu.CzQ srh
2.O'
g)-- 4-1.5
,r4rur&ffr*t
7. -
PAEIruKAlWr{/tAlae*gruEAWEBI6,frr4&tsELITVArd
Ol . Sebuot6 Tan4kanao dlerr[dto tndUk*ang V>lO henw t 1.e6tS tanti p=
o h* dan ,guotVl bab^ratl t'an9 Wombe llsao Sua+U begangan t@frJban
Sebesa'r {,o6rn IOE Volb.
Tgntut anlah -,
at) f sebaqat suaiott filn4Ja b denTao ofigqa?ao tatUtar dlLclLU+
elaq T zO pada Saat t =-o .
il Arus dorlatn .eadaoto vta 67nb4? Sebagott t;^,atu f$n6 t r
lN otkLu C ao g g ztP t fn €n d.ekabt V a,,k *PrbtCI I Qat).
Otk: L = O hgn rg
F: Bo Ohry
Vcv), 3o stn [o u uott
ptL, d T sebagat Euatu f-{,tngJl F=+ T=o 9 t>-o
d Arus darlarm ke a dar 4n fiant o* * b -' **
)awa'b'
to dr lAu +8o1 -- 9o srn tot
d(At+8f : €Jt'l toL
VLil =8, &(Y) :0 rtn tot
r-: e-[vd+ C t"J?d+ . O CO ola+cJ
l: e'fsAtE f essAt. gsttr 1otdz*ca
= e -8t C g teBtsth loY ol++cJ
r e-Bt
tffi (or,o lo!-rocoslot) +.)
gnt,uk t->o 9 Saa& E=o rnotka ?e'"'satnaao
T :9/t aq CBstt' lob'(oco's'(oe) *ce'Bs
o :4fi0a (Os(h to'o - l0 cos to'oJ'tce-d'o
o =gll6aCBstrr
o -to cor O ) + Ceo
o : 0[&e CB'o -to'r )+c
o>-gollb4+c
c = ao /to4: Lts/82
.-tJodt
,
):-, = z lto4 Csstn lob -locos Pv)
+ 4s
"
e-BL
Ta
6! s21ta9 wr7o)adt't
,,Y,)z; N:tr:L:"
ggfitn04a:
t =3 (Ssrntob -tocov PY)
rA
tfrL/E*{,tWt
8. /'-
PA[lruEtlK n{rlW,rgm? truggl 8,rilr4&4 BE0fi AZrd
bav L
2'b. Soat Lai+thao
Ol' Sebtrafr ranTVo{^n FL .tePert{ qotmbac
/ts^m ?ng - JtKa attKetahut y =G 6{gnrU'
restsbansi ?= av ghltr Aolr. .suatu ba&ecat
-/an9 mefftber*utn Sv6 tu yeqan%n Fon'Sbart
Sebeso,r bovarL' Jt!''a I =o, Pa)a 'faq{
| >O Csaar Eaw[ac S d'tWbuP)' lentukab
t ?qda .sa6aE- b '
O&'- U : A Aenrg 7-= o. AaQ E=o
@ = a.{ah; csattctar sJttrri(tP)
EcO -- 9o votd
Otl I Tentukao .t ?olo' 'tac1+ V ?
Jaaab. L A((At *Pt: Ecb)
p:grtOhtr
'gLk)=TovolL
OAt/dV+eut' zo "n
&|d'L +qC ;5
?c+)= 4, O c+):5
'-,
' e-Sid* t 'fei?ab'OCd
dt+c1
= e-J^ot f [nt1d+' s AL+ca
= e-o*f !eo". EdL+c7
_ o -ALr s/qeAL+cJ
-v L
- 5/a + ce -4b
ilnbut L r-o ?aAa taato v>-o mo'ka A?ero@h "
J: v/<+ ce'AL
o = vlqt c' e-1'o
o-- gla*c
L'-e/4
I ^t^t -s/q e'4b
pzaka, 1 ?ada sao& + adalab t L =
b{4
rt{ATEilAru*
9. PA[lIEffir& r**Wr*,(rue il7648/ BAnr6# EEEITVAr4
0994, rc*tY) = X 2yr+41- +6v+Cr
UnUU f Y> -t t SaaL { =2 t try1d.lcar,
*"1ti4t- q xlrc
2-' C-t), + A. 2z * e. c-12 :C
-a +tb-B=Q,
1=C
Jadt', lersamaon a(tFeren stodn-/a ada(ah, f z/ )+ </' -1
c) C'/o +zxy *12 )v'. -y2- zf'/ +,X2 '/ f:o t saatL Y=/
C/2+2ry--/")d _ *j2-li s -J -->tY+Fz
f _-t?
u t -z(y +t'-" )dr. Cf2 *z*v _22) ol|
C-Y2* 2t'y +,(, )df - eN 2 *zfy _72 Jclv=OM = C-.U' -z-Fy +rzj + zt4
ru = c-.tr2-.y-,+y; ; *
--2Y-eK
n-* ='2*l-zY
21.4 _ zP
-a- -t7 ?'9 eksak
21 2*
FC+.-r) = JMd*+ cCY,
=Jc-'12-2t'y + y 7) d r+ c c-/l
= _Xyz_x2-/ +t(bXb+ cC-t)
-le(an)ut nYa
{r=aJ tv/r +rtcv):-Nc t't()2/
- 2f't- xz +cr ty) -- -r2 - 2*Y +12
clCl): -Xa_>xy*y2 +z*-/ +X1
clcl) . Ya
cct) =
la Yb*c,
SehtnlQa r t Ct ty): -yy ,- t'ly + | (Z x z +^lel 71Ct
Untuk *-o , saaL ./:l 1aa.ka :
-XY' -tua +,(zX7 +,/>-{3 = c
-e.rt-9r., t'lo O3+ t(7.t3=C
tla - c
JaAr', ?ersamaa.o edteeren .f rolnyo qda[orh:
l'-x "/2-' x>1 +'lvxb+ 'lz/v= t/z
5Y.74 .
l44T'g-.Ha Tt ls4
10. -
ruU774AWr{,4W'fKmeAlE44ErB'fi1f6ffi EEILwYf
,l -bf " -() d* t Ct +27 -Xv) d1z-o
M-CZY-3X2 l) - N
=^Zyzz./
N-- Cl +2-I- Xl) + zv - _ br'
2N =2 N - o.t) t*tZlL:' =2 N _) ?.O Eksark
z1 7t
t=Cf r-/) = .J $dt I cC't)
= tC2t- >t21)At+ cc-t)
= *L - l3-/ + cCfl
Sel an)uL n-/a , .-
{ - 0 SN dt t rt (-t) _- N, l*rt):. -0 f,Nan +d C-t); NC *t[)7Y -eT
-X) + c( Cy)-- * zy *y3
c'c-t): t+ tl-f 3+x7
c(cy) > l+27
LLn)=.'.l+'t2+Ct
S€htn99a r € Ctt-/) =xz-x3Z +y+y2 4ct
Qerarnaa"n dl€eren $adrtTq aAaila.b :Y7-fZV + Y+12=C
B . -fe[AJar +<a^lah ?ersama.orn dteer en&at ek-satk d.eng617, S'{oLraL
babas 1an9 ettber lkan ber[KUu :
) Lz71t+8i dt+LbrLl$+s)olizoi y---t ,saaL y=z
O crL {zrt -y>ht = --/ 2
- zra +f,, ) t=o r Soe& y>t
J a,aob ,
) Cz*-{, +8il d*a Lbt<z-/'+s)dU. O r y= -{ rsa+t *>z
ft; l> *17 +Bt) -, q, > a*yz
Nr -- ca f ,'tri,g) u * =-
6;u.-/
z
2'l 2*
cfrl) '.lu d*+ ccv)
=J c 2 *y 7 +gi d,* t- c Cy)
: x2-f a+ 4tz+ cCl)
Se{an)u€
^-1a,
"ir.:!*1" lcrcv) = Nc/ry)z1
a xlY' +cf CY). brz yr+s
., a( (y?. 3f * 1'+ s - 3x27'
clcv] = 5
c cvJ -- 5Y+c,
fraTE Nnr[M
11. PAEITEFaffi lfirW'rfim9 ilWdEr Bsftr4ffi EEEIfAArq
1 rt.y6-tt +aY _- -- . cr)
+ ?OL hsmo9oo
./,t + @1t +g.t =O
t (er5 4rn aao ba.nLu
(z+6r*e=O
6 rta) c r tb) =o
f t =(. 2 2-,
+ ?enge lasa(ao urvlUrn nOmO get
Yh, Cr e-bt * Cz de->'r
+ Fungsl Percobaan
-l -- Ae2'(
tl -- L Ae''{
yr( =
q, ftezf
+ Jubstrtust Ke Qersamaao c) 6ttpecO-(eh
4Ae zt I GC2Ae/t )+ E Cftezt) =O>/
4 frezt + lz Ae'r I g Ae^ =eLx
25Ae'* = €"
294 = I
A=)
zb
+ De:ngelesa.'l a'o [.chuSu S- :
ye = t(zs Ozf
+r [enU elssalan umu m :
-/ =
yrr IYP
' =L'r|-=*+ cr- fe-bx + t(29e2{
7. t€(psal l..o,rrlah QeYramaa'n rttFeren{tatl e{sats bertku L I
a)- 1zt +t) clr + Czl + *) c(Y.o
il. gzr-zrrt)d/ + ct{zv -rz)A-f -o
Jota^b'.
a) Lzr +rJ d*+ (2-/ + r) dy.o
M=CL*+1) -rg =t
N=czy**) + =I >tz*
7r'a - Z! p p.O g{qsak
'V'l z x
Fcfr-/)=.fMat+cCY,
-- t Czr+-/)d r *cLy)
=Xa +Xy+ CL1)
SelanJ vL^Yor
Trn' a.d"t { c I cY) -- tu c r-t
27
X {ct C:) = 2-/ 4*
Ll ;l) , z'{ { *-x = 2y
c|'l) . -12 *c,
Sghr'n 44a , TC rr-/ )-- Vz+*Y{'12+c,
f,)ersamaan drfFe ren51'( nY' adathh
X2+ XY+12 =C
rY)
Na r E"{4 A rr k4
12. PAEIZEEIl78,a{'filAFTigIWAWEEIB'$r6&rBEIIfVArq
N er m4 4T tlcn
b) -f "t+6y ',+ D v, -t, y =o
t ?ersormaao b a.otau
g?qer, +gr-t2=o
Cr-t) cY+4) Cr*>)zo
F1:t Vtr=-a V13=-3
+ ?en9 ?l€sqtao Llmu m
Y ; Ct e t' + Cz Q -4{+ Cze-DK
fletod e
rG
Hornac
5 -t2
1a
7 12
tz +?r *lz:o
t2 4 .*.
j+
6 . Je(asal F-ato Qers^maao attferensl at Itnter non hornogeb ocde
olU.a lzer tKUb I
a) I rt_
b1t { 2-/ = 4.e- *
c)1" +6-/'+ q-l-- €2K
J aaa,b "
;;'"ir- lv r 4rY - +e"Y ct)
+,. ?gL bom} gett
:1(r_ b1t + 2y:O
+ ?<rsamaoro bontv
(2-bc*z--o
Lf -z) 6r-() =o
f r= 2 {'rz= I
+ p enYe ($ al ao umu rn hom o g 96
th =Ct€zt'pgre{
+ Fungsr Qer cobaa'o
1=Ae-{
Y'" - Ae-Y
Y'(= le-r
r Jub.rtttus( tse Qersamaah ct) owero(eh:
Ae-*->C-Ae'*) +ztAe-*) =4 e-'/
Ar-*+zAe-{+2Ae-Y=4€-Y
GAe- Y
-' z1s''{
bk =4
frt 3 =7b3
'd QengeL€soilqn lchuJus :
-{g = Z o-N>v
+ ?engelesalqo (''(rnum:
-l= Yh +Y?
> C( ezt + Cz Ot y Llzg-x
13. ruIIZE&tK rfr4fraFri€rW nEqEEI BAild&, &EIITVZr4
b) Z tt-2--/l + y =O i ..l=t dao -{(=Z Saa+
+ lOrs a,maao bonbu '-
rz -2r +t :o
Cr-() Cr-l)=o
f t: fz>l
+ Qenge(esattan urnu m
Y cCrel'i + Cz /et
+ flntutr< Y=l t rnatka:
Y=CteY+czN€
1:Cteo+Cz-Oeo
f=Cr*O
Ct=!
+ tln+uf Yl= z , lvtakA:
t'= CGt * czyeN
Yl=Cr et+ Cczer+Cz*et)
-/f : Cr ex + Czer I Cz't€(
2: Cteo+ Czeol Cz.Oeo
2: Ct*Cz-*o
7 :- *Cz
Cz = 2-t = I
ft^Ka:
'?gv
1z Y; Ct€ * + C'Ye{
--e* + *.e'l
b . Selesairlao ?ertotm a,to p(1 Ssrgn.cta ( [tn t€i hom,gen ot d€ tlngg I
b Zr tkub '
d y rr-4:rrr+yr+ 6v.o
g) l"' - Gy tt
+ byl -12 ..lzo
JauJab:
r7 rt(- 4y 't I -1t l. Ql :O
Qersamaa.o bomLu
Y>-4('*r +6=o
rletoAv dorns,
1 -4
Lr-z) Cr t- 2r-3) >o
Lr-2) C r'a)(f +t) :o
l-r;2 Vrr-3 V 13=-1
+ ?enlelesalan Umurn
Y =c,e"t Czez*+Cru--,
f=o
r2_
-)
2t
L'
- =O
2
t+
-/.
N4f,e.lU,*rtlc4
14. ruLrffiffi& il/rArOT,fEmB AtWEgr aAnr$A BELfiAZTq
4. Sele(att aoln /ttfer etulolt ltn
oeogon 9a^raL babas Yan g dtbettlcao ber tKuU :
a) f rl-3'/(+2y
=o i 1=o d,an I = z saorb *>o
b) .t rl- 2-7l + y =O i y= I olan 1t> z saa& * >o
!aoab'.
o0 Y"- VY I 1zY=o ? 7=o "lan
-{t= 2 gaat r=o
?ersamaan ban lpU :
(2-ar*z:o
Lv-z )C r-t ) =D
f t:2 Vfz= I
+ fen9 elagatao vlmum
Y: Ct€ ,] + C>er
+ Untuk 't --O, marka "
-{ = Cr€ 'r+c z €{
o -- Cte 2'o + C-€o
: ct€ o -l-cz
= Ct *Cz
Ct *Cz >O Ct)
+ Un+Uk *flrzt tqYa:
l= Cterd + Cre*
1t= 2Cr€2r + Cre*
2-- 2 -CreL-o+ CzSo
=2 Creo* Czoo
>2CtlCz
2 gt 4 Qz> 2 Cz)
-* E{t m nas t ?er $amaao Ct) c{ofi CzJ
Ct*cz=O
TCt *C> >A
Cz=-z
+ JubJlttuJl Ct-- 2 Fg ?ersotrnaa'n CO
Cr *cz>o
z+cz>o
Cz= -z
[Yatca :
?DL + /: Cre't*Czev
PIArE l,tA r?'1t<'a