asdas

1. PO'ITI]IffIIT XIANIIIIAITTUN NDGIInI BAITOIIA BDTITI'NG
j.
i-
i)
i)
i
i.
6Ab 4
{ansEocrnad laqae nvers
b.
c-
s
v
=)
/
2
T
, alu .1
s"-(alz"
./ 4/z
4 ,"(4le)*
6nh 7t
='u, .i,
i'
?
2e 1
s'+4 s2-q
r cosh at - a/e dnh
4
.vs..,+J_
sa+{
b@92u+
:
e L'4 x+ol
L s]+4 )
q/* <fa zt
e q r't*),isr"nat
*
t '{ --eI-} = I cos 1t
L s'ttu -1
-
L-'{ b ,-Z j'
Las"-iJ 3 s"-(a/s)'
+

2. a.
-
POilI'BIffIIT }IANUTAIff UN NIIGIIRI BAITGITA BDIXTUNG
b. L-' C 3
L as-G
L-' C ns
a
L s'- 5
L-'f1I
uqs_1
+ 47
-r
s"+,5 )
l
L>)|
-7D
s'16 )
2.L
Scos zt + 3e'"
ar?
bY
= 7- e-- + 4 st"n 5v
--+q
4
{,"s-'' lL < s-r)'+e6 J
L-' _L = cos fft o
s'* ?,7
4
= 4 e"'- a aslrr. 1116 t+{osG
K
'a=
I
= 7 ash at +{u- zdnhx
c. z{7
s&.. .lg-t
A 3s
s3- to
+frL
5..+b )
f
6 ),
s"-4 5
.t
e. l' .f __ts_ + - 4
L s2-5 sa
@a L-'f 3s-z )
1t"-"t -r3 J
r'fbs?)=1
Ls"-4s+4)
sn aqa
L-r
*
i3

3. P O I.ITBI(NII( }IANUIIAIITUN NDGIInI IIA]YGITA B T]IXTUNG
@a s'{__J
, L(szr[6)')
) f t ) =-2s<->
)s L r' r<- ) Cs't4')-
tqAt s = -!- A /--L-f<r ( r. .,1,f- .z As s, +<' )
kare,na L
tC---r ?. = rt"n'<t
L E, vq'J I
maca ftH
L (s't4')' ),
a L.1
-'{*(di}= _t L
a
L),E
)'. bt.
r''r E
l- (E,-f ,
)f_
As Ls"
laAt q'
(s a*r
karana L-'
r -l
rn4K4 L
b
t dnat
Lo-

4. a.
P O I^ITBITN I I{ }IAN UTIAITTUN NDGIIRI I}A]T GIIA B IIIITTTN G
c L-'{ s 1,L (s'-q)- J
A / t = -rc
At ts,-1,) G,-A,
lalt s =-t -L
Cs"-*)= e As
kareM L-'f I ) =
L e,4, l
I
a L-'! ) z
L (s - D)'J
a-r--!--:
As L s-B )
taAi ? =(J
Ce -e)1 ),s
t(arQtra r'{ lf =
G!
(naKaf'{ 3 Z
I c,-9, )
nvxKd r'
tfu| = u*,''
t+ *) 3
{ sinh at }
L ?)
,1
r_l_t s"- z-/
rinh at
?
= b s(nh at
-+- b
4
t{L
-l
G-a)-
-t.4 .
.'*.
I

5. I' O LITI]I(N I I( }IAN UIIAITT UN NEGBNI I}A]Y GITA B I]IrTUNG
er{ = L Cs -s)rJ
) / r = -l
;sts-r/ G-o
taAr eJ =-24
( s-r)' A s
kA"nA ;'I- I Jl-
Gt
-r.L-'{Af | 7
, L As s-r )J
-'rCt)'- t'-e*
-eb en
t7
s-r
=e*
6"
naka L:'{ , Z=
L ( s-c), )
=
I
a. L-'e t ?
7-*"ro
karar4 L (-Z- =sfnat
s.tg /
€$.'
rnaEd, C'f t
-_Z
= f?inatlt
Lsk +il) o) .'*
i,
,tI
tb@c 7+.:
)
_t
7
I
3
(cu lb-r)
(t - cos?b)
F

6. P O I"ITBI(NI I( }IANUI'AIIT UN NBGBNI RAITGITA B IIIJTTIN G
b-L-' f 2 -)
L scrrly]
karcna U-t (-f- = sinh zt
sr</
r{ut<a f'{-=--Z = fln6 zrJr
ma1or'-- ''-
= **il 'b [:
-'+ Ccola:t- t
)
c.r'{ 1 7 =L s(s-a) J :
. karena L-l (-l*) = l ebb
i
g-t-/
(qKa L^
{ 1 ?, = (, 4 qo,At
L scr-r) I J
- 4 obb |t
T" o
=4 e"-L
b
L-'c E ) :
Ls.Cs,+rr) ) "+
karanq L^ f r =n'nrt
L <, +rs )
,'.Atsq L-'[ u a - f (, rfln ru Jt
L c= (r'+ zc)) ory
;'f'
- * c'es rt At
2 +"'h5tl;
+ cilc+2
€d*
A,

7. P O I.ITI] I(N I I{ }IANUIAIff UN NEGIINI I}A]TG I(A B DIITTING
5
i;
{-
i
:1
;.
e. L-t C 2. )
A*t,uT
t<ar€,na L{ /--g- =
lr=*)
a
(7
Or
srnY r,ll t
rnAK.AL-tf 2 7
L r<t-rt = (t(' , sinh rt3 t Je
ilJ ..{=
= (E i- <osh rl5 e Jr
o);
: - dtnh (Tt lt, 3G l,i
b.a- L-' f1.t_
t
i1 W sinh {3v
74?
,Ef -au z(e-r-ry.'
' I
=J e.e au
o
= ('
"-"*.
eu aa rir,o)
= - Y e-uu- ,* l:("
= - l- t d-o'. er*' - | e't '-l
La;)
= t e":L e-"'
L. b
( sta) ( s-r1
=
I

8. POLITI]I(NII( }IANUIIAI{TUB NIIGIINI I}AIY GIIA B DIXTUN G
b rd-t LL (s+:)' G-il 5
=-!3
__t
7
= _l
3
?. 4.L-'1 astt6 )
LEJ
4=='
stn g. C+-u)Ju
o
srn 2t
{:
r et'
aF
3b
e
rG
cDs - 2u lo
-r1 ,,
ei
-)v
e
-ru f
e
-Vb
e
coS- zb -
.t
2
lo
srn.2t
l
3
l-
I
'l*o *zb=b ,1'b=-z
| aa -)b= it-
rfi,...)o /
I
.1.
( *,= )
+Ib
lo
' srn 2t
.--
.ii
+b
cos - 2v
€d"'
3s+tl, = 3s+(6 .=A
gz- s -L Cs-7)cg+z) I -3 r+r='
' .. .a
3s+t6:acstz)+gG-t)
ast[t =CA+B)s I z4 -zE-
A*B=3
*A-38=lb
A +g,=3
A.-+-=i
A=i.

9. I' O LITIXNI I( DIAN UFAITI'UB NEGERI RIUY GIIA B I] IITTINC
;'f vs+tb )
, T*-'r I
L-t f zs -r)
L tr'., I
3S-l = ,s -l
E'7-z- + -, .?
-L s-j s+> )
|
-,2
+ t L-'/ I
I
s L srt
5
b
q e'u - ., e-"
4
A +b
s? - s Cs-t) CsCs+t)) Cs-r) s Cs+r)
t
' ?s-t = e (9cE+r) ) - B cr-t )
as-l =
Ag' + Ce+F)s-B
b=l-+f
rt-*g --*
' k:l
L-'{ rsAT = L-'{ | +
L sl_s ) L s_r
(Elr- -t
= e- + Le
//

10. PO I,ITT]I(NIII IIAN UIIAIITUN NEGIIBI BIUYGIIA B II UTT}NG
c. v-' I stul
, L bsz +?s+> )
S.t-.=A.+-
b9" +7s+7 bs+* a.t+
s+r r ACastr) toCas+>)
9t = a*s+A+ 3Bs+2b
2A+w=rf tlrr*bb=l
4+zB=t f '| +*+qo=z-
-b r-l1
Bi=l
L-,
4' * zB..=
A + aCr)= I
A = l-z
A = -l
, -2lz lo
)-i,;
-/
=A r D.
s.tJ 52a4
+ D( +4s
e
A. V-'
{ rr -trt 1,
' (s+4) G'+a) )
e"]-tr9 - Agz +aA
I
$=
?.nr+4
nA + (
4A

11. POLITEKNI( MANUFAKTUR NEGERI BANGKA BELITUNG
{ o-? - taE ')
L cr*4 t cr,n5l
ffi+L_ffitL-'/-l-raL-'r tL
(;i/-f,1 t#
<'<b - ia-j E,?r at
3
-4L
e --4cfir
)t
L-r
r'
7T
I
=7>
I
= lf
-
,s-b
L-t f 39-rr )(--
L (rtr) cr-) ) (
Jr=-a ,Jo=3
?cg) = as -rt
qce)= 52- 9-b
&tcs)=&s-t
?(A)=aC-a)-n =-rs
V({r) =rCa)-n=-9
&r (x,) -- * C-a)- I =- e
$'(+r)=sb)-r =f -/
L-{ 4s+n7 7C r-:)Cf,rrX str) )
/t rJ;J2-=_t ) /7=_e
?Cs) = tye +)? i &cs) -_Ev+af-
(9'(El = aez + q9 -g
? C/, -- tq. e t 4? =?5
? (dr) = t{C-r) r a? - t6
P (,;a) = t4G:)+a? =-?o/
B. a.
=J(/,)
o'6<i)
J,E
6'Cy', ) = z(z)" + b,)- e = ts
A.' (* ") -- ? (-t) 2+1C-r)
- 9 = -G
&' Co4) =ry G?)- + 1"Uz) - t = to
1-rc nevll )L' 1-cmcs*
= ? (*r )- enrb + I e) €rrrC
Q,'C*r) tq,Grr) 7
=+ u'*+*e-'+ -za
= 5 e'b- 1 e-b - t e')v
b.
f

12. POLITEKNI{( MANUFAKTUR NEGERI BANGKA BELITUNG
+t
) Cs->)
) Je=V
s -6 ; &'cil--vs2-tasf tt
z 3gz- GS
(s -t ) Cs-z
=l ) Jz =J-
=g7:Gsz+l
L
-l
-t
L- 1i zs'- r-s +s 7 j
L St- t s. + tts -, )
Jr=
?Cs) =rsz- 6s t I i e.cs) =
? (;, ) = : Cr)'- LCt) +s = |
?(oz")= eCa)"-6(:)+e = I
?(*r)=+(a)'-GG)re=D
&'(J,) -- l(r)"- (aCr)t lt =z
&' (*r1= aCa)'- ta(z) +rt = -
6.'(*r) = 3C-:)"- la(:)tt =
c.