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rico
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f £. v—
9 fezo tm f-55 prrnta , MARAU ALLOUNDIE MEC ENADE CRE -
AMBITUDÊES Cop? Emo a fimo . -
MOR VELOCITE: Ly = mf =(Sonfasas), Ur ASTM [DS A
Mas feicumAmor: Ay, = ap elo i2sdd. Oss Pra dé Ens Tas Wong Are
12 A atri! Ge tepo am tmp? DZFema: Emma,
Gr Perg = OoRemfs Roz mb? MM = Mm,
Ee mo CRmk nf O DMI Empr OS
- A, + z «EM prE Êo dito
Bat mt Za fa fem = poe redh
Drvçe Ela) sp Eat): iam SAS a Ze radio
PP ozak
Fela Ago Xp”
LD: ambez Embdo radio) « cvog= EE mea)
Ficuemer er cora Toys doam Ro n/As8 us"
DESA - = Rd a.
Ê fe siga A sx XE hi 2680 at) = n099ub! ao
1923] p=42s -27 22 SIE red = Rj torom
fr s us: mo bl REA mo (22 =oomarso
Ko 01383 EMI) Voo Lopo CUBE a NS 2a8 ras) | DR |
. a + Vamt O OoPads
Gm Kmp = (01850 NE: 288 r0dh) p= EP mate 128 | ;p MOTRM 15 TO GU SIIFAE MEIO, THE
IPS [AEE Em BM W= 25/b Catent da Cesrademo 117 Gon MIA tr
t + e THE SPeime. THUS «
Femas Rue od trÉrco For ame x rã 3 on
- E me) AMO Emi TE mm m ”
Zuost p'eDo = 2826 = a
PO Po Tiga PEIES rodh Eb ÃO EB doors ce) po
EGMDAS Vus Emp (IBN Ibo red)» 48.16 july pros rd qo=m4ap redfs
Up= 40
. º o as rom remo: yet gefinco
- : ra
Pla fala drsos rã TVIZB def Zames £ 2% Ragafma (r30,8 radipaliz. so)
ancas 4 Re g210 Mm ResImm A
+ = Elm = Us, MES ink, W=706, | (6) Mencuee THE DietAEMBT KJ+ To contoem
. 5% ks
AZ É=O; X= km O0rm |, Ang arés >
>= porra Zeus from Fis 187: e gm
ER(17.08): me EO o ATÉ ces: pl=( 087 mdkouzc)= L$22trd
sido = Ef 24078 radk) or EA ate nsea
Cn = R.A89S tm, ke 228 sd
Cy Um “a (2 2840 0( se e) From EG (tg):
7a FE IR OF TERT
LE SALE) = (00050) Sim MOSS = + JE IBIAO mo
126 LAT. Bem 600 rpm sro JZ0o rpm , “me Aibrantund
cm mo PER BREDA! 19 HU DUL TO BO
Led ».boa Spam m EMBER red
AREIAS. Boy % mpi ap
po sê "TÚGRA)
Orvob sk ft
w = SL. gon20n pe
= coz
» fras. gnt Ta ”
sz: *, “faso "tres ao dj ur «4
00978,
Wp 16 rpm = 128. “up radh
<a lisas): o Em 7 Do asa
As
a % Bo denaai om aro Som E]
«a . o
- “3% 1878 mm «td
(Bem eoute: Porn) -
| Fa LE DRA nu - =
E 2 P COS (PEV = pra m [pa 7 ros) cas 48.484
=— 0.890) mbe .
= 84 cms? - a
“From Cafu):
ae p Empis) = fovremf1308 md sap Megane
AMB
no = alta mat =
FE
1992 POR ASS = SPEA GASTA 4
1941 conrinco
PVE -[2eoee 03.06. mede
MEASURINE THE Dispencêent E | TO Contoem
WA FEIRA, ME deus
AT Xp SO mm = OSm
pê=o, vHUS, FROM FE 1; pobre?
(o) nFrER Cosme HAS MEVED Sm UPAR,
+ o u= Lg DOM = DOS 0a —O.OREM
From EGUIPIO)? KU Roy sintpétg)
-OL7sm = (210400) ei (pt +49)
swlpisdr-as
plrdrro plo g zo! = 120%u BE rad
Hb pts
PC Ism
É= *Omns E=ó ses «É
(D) prâna 250 (9.00):
Vo mao Cosfpt 16) = (e.0 5 V 12.416 radh) cos 210º
=- O SBO? onde Vero sm)
Fesea EG UP:
= RR7o
From EQ, (1910): .
Xº E SinbptrE) = (RS) io PRI 2229 io,
V= Fpp cos(ptva) = -(E Za E 4) (24,078 rats) cos aro
FRA EF(II AR)
Asp" sinlper a) (EE RX2R OS mdbfisi 200º
= +10768 Pa asas
K=2RIm aovE AQUIL. FosDo
Feys vp, A
[César me) eu
PlE- Ca tara tm) hos rd
MENSCEA DIE DISPACEMENT YE TO covraem
ora FEIRA NE DAVE:
AT ÉLO: X=%y= AS = Ep
péro, Tres Fem BER: pefr=
(O) AFTER cotent MAS movep E sa. vPRARO,
+ x Dd Adm OS.
From EPI) = Em Sinlpl HE)
Onsim = (Pas tin) tl. CPE TE) .
sintpitójemnz
es É Pr LES, BO PÉ CIP E N68. PO! -
qpb= DErE'a nesPt and. —.
L3top ras
28075 radis”
a (19,4): .
Ego P. costré ag)
ALI ide
=oostoss | teooss df
ÉDEN plmtsECDA ND firpossraus)
For LOMSPLZ)? ta) E PO 67 - 5
É > es redf
aaa olpt ro) (BOSSA raio ro? Macae rom /lsea re)
= EASO fa? asssmeiy 4 Ted go *OI8AS roxas 4
[/ DIO | ron smass- Dem sesta: f& < SER. 1254) he fesassaa
Avi Um =
1212 For A sine tono P
É FHE TOM ALONSA TON OF TRE
, SPlmss at
Aya o tod, Ss PBP £
EB Fomr” do blá
Ag = 10 todrô,
(0) For Ema b2cid, = BE
Im =(L28 pels.s12 rodb) Ez 0887
E). £
EPE Hã E Eb,
RÉ = ata = 70 6/08.
19.43
perpã=)
(22 cela radio ara seem A
4E7 Pee cromc Forces
PEQUIRED TO CAUSE STATE.
DEFEITO E
Pe RASA,
= (Sta tac tha. 0 tb JA
P= Cora
480 ABO JafRE e
(Howffaz arde)
— Fera a -
App sitpira) (E feno jsa tis -
[a Pni6 seje a = 282064 7
HG | | flats socozom or Flog 9404
ET - PERO medo. ps
HEtms fi = BE.
AZ £= Grresa.
qéxa = =fenore radio 16) Z red
= SU8Q yad = 2H nun
tconrinuco)
Seas
000000000000000000000000000000090000000000000900600
19.22
Str Sour or Pror /2Ê! For
Deriva TioN or eo)
RB (dj 3 Fog L=0.8
* = SE (SA H O) * ca «af 22 943
Da: d=08m, h=orm, B-600n/m ha = 28) mk: = 75
(atom Tross: gp. 2” aus:
gs Og rm p= EE (po9t8 e)
o 2 2% 5 sy Usa TRUE 49,14
eo (47) = 2600) [0.5 -57 (a) For smp. oconrunso QzOS EE =,
mo = 284) Rg m=388 4 TmAImes -«
É/9.26
colina v=%ElenlE)
(1) Fa ro mems 87 quo () toe enr3o Efepor
cad): 2 2% Tedlormyp ses) JEAgaSs «a
a sa é EK
1 Bk-jgo
me Dc gastos mesh, 4 (1) por emo ve Lad
y Telidgokp 19034) Tears
BM
See . ZK £)
; é YI927] 2a (20: E erjz)
me
e g For Lz06%»
£- S8 -
Sd Er From “staromeo Mamempricnt. Tarado
+ / SE 40; GrfgrMs: K=ssto
fã tr VE « > >
75 Exfutma o) CM rog43 4) FRTOSA
X1224]
Jz da
5) SE
4 Ní- si Vem) sin"
VLINE THE BINOMIAL THEOREM, Wi WeRIRO
-%
oesgreo e [1-0 (Bo)ein 9]
Visio de beinig
é = ge) sip see
Indre ME MEGELCT TERMS OF ORDER uemro TUAS 2,
sErIme E “ho flcos2t), me mma
«Ef [rem m[ttr-emso ap
= RP redes = fam Pe casco)
Elo + Elo Bp poi cn E
=815 [E + plage) E 0] :
W=R7,
Kg (t+ ford) (28.0)
ma bh, = 270 Mm
Ja e
a
ves | ME À asim
bc ism —
mec Fa Blyria)=R(086+ E)
ma-mPa =fthglossm) &
Foz filtro E
(0) DEM = TM
wíges m)-Flosm)= Ta rmã(o.86m)
wwloas) - Af0.80 + Room je flooS JE stored
BUT, 4 EQUILIBRA, WE MAE
. WIOHE)- Rô(0B)=6
Zhus -(160 Yos)b = [é tsP estos Jê
22833 S + 4s08 O É rz/3.02 60=0
pe ASP rh
a
KIZ25 me: pego
For mei aseutnrios: 527] me Pe RE. RE MOSS Feasso sa
we ms Teo T-foefE =. > sro O ATE
MSIE THE FORMA OF PROR 192%, WE Voei7E .
re nb? Ff sit Bm) = Lo) % - arena: iron -
- Eme A Se ko = (40 e! S9S rate) = = sus A
28 = Why == 004; Ene Ad m ”
sm go = ufho-i)= 004; smBh= 02; pu assento
E
HE Bia snJê =
BOT IN EQUILIERIOM,
(us sto -
e 27, RE
Care 8. mt O
mã mf Geasn)6 -
MelLErs
ge. 8
(0) +27M= 2(M eg:
wo gxra)- Fltsr)= Ta malas)
Wlo.as]- ALSO + Sa SH)= me + EE tos)
WE pve
3
DE é
sas é
Po JRR mis
id.
Ui
1929 1-; fez 9 bj. =48 6/85 W=156
- tád= srt
Bu, = 0,28 pé
A
ORSfE
une Pe Bixtd)=Ali£O +84)
328 JS 8
+ mlozst)- RS ds tá) o
TEME, o9220 á
E! o
7Hus: pino a[-
E +(312)o=o
pesam qo=1873 redfs
reass 4
Go Um = (0 tn 1,936 rolo) = 297% do,)s
Oss 4
[230 COMTINVED | 35.8, = Enade +
wins se Jo plo ssa) = Tia + ma (Sra
wine):-Aoaso- Separe) e Ea PÉ els EG
Ber 1 EU IBRNM, WE sine
+ west) - BE, (o,832) = o.
mess. A (osso - fuarvasrernm [É S
2.
(onda rante) O, = tur ê
(a) É +27 O=o
p= dez2p pPelzrm rodks
ye ZE. Z2 = 049/05
P 427% radts
mods 4
lo) AT EMO A: Log= OPSdo.
Von Ls PONTO NUR DI ralo) = SPP ips
Eme LO falo AQ
I973/ rep m=s Bo RB= XD Nim
+bEM= TM z
Wirsingj-gr= TG +mar
Wir sims )-ffrrB)r imã À mar
BuvA w EmuneeoMm, WE HAVE
19230 | domenst
=.
| DISSO Moça = Rb
a:
sPeme: R= 30 fio =360 16/48
Y-re+áp= oBI376 Me
F=hx= Rossas o +53)
RODAR: Vyg= 0E/b deg= BE.
ma=mlietti=
Za -dteie uses s
LEE.
re obs a
F 1 tem
Lou dO fo gs38e8 PE
e ger Ê
(comu).
jo co dm cotess ocoges dd
48 iyfrsez?)-Ldar=o
TEUS: -taregimremrja
=x gm
g+$By-o
. 28 «ZE
EAR r=-[5
=| EPRalal = Vão = 10 mais
É) 47 comem 0E Disk? em 10 mm
Sr Tm PE VUO metro radio) Uia 100.0 mnjo 4
NorE (Esurs ARE INDERENDEN? of
RAOUS P OF Disk AND or +
THE SLOPE O CE THE INCLINE.
vo ZR THE drerrafe Tersso Rr do ú
ErE-Aro FIA + E 4 ug
e nrkrá 5 Ju
e ctg =" & 2
Do ty Lo
R (E bay? a
rel A * é
mec, Fa llrida)= ALSO ráci)
. mã = mfasm(b-E)á
+JEmo! promr-I8 Tá
. =gnig
-“(ertrarltm-Rre)os 78 A
gd or . a) DEM = EM ops
Sr fera wib-£)-p6= Tur ma(b-5
+= ear (| wie E)-plbo Sab = fm Em b- 45
sara BUZ ly EGULHERWS, INE HAVE
»= 250 83 = 1 Mto +? wWl6-E)- LS, b=0
TE ess ra cr me 4% «(4 mettom(ó- 6) é
2
7a EE: EE SE = 47 vedi gif o “ls
pó PF 7 . e+ dom em(6-8)* S=e
Le), RAr* 2 LUSANinionsm) st
p= 5 formato) z + = E qêao 0)
Z- 28 1 Rgm* (e) For amina 7:
or sue Tom? & Lbeteo-gPJrs- e2[uto-E)]
mos) 28.479 com* ? [Eee ST
É - cisco m Ê = 400%
dote 4 Altas sf (6-4) =0
Joke, AngAS vEguer: IF Pont Ce Puro Doom putas dl fe slrdaco
HO mm Meio pe Fecnsel, a 14%. L : br 34 = 2/20) = jo
Se Sl dr A im )* SEIO vad mec áéteo br du Sfi0h) = 20d
=0
() suasmrraze bm 2L um Eai):
tome En “iss, 8946 cutlorn sto) ca? ê a
domo tn R cg tl Ei.
1.33 ACE
SHE Setur or Beor JR DATAS = IE, R= Bl = 48 UHE
DATA: = Hm = ne dMfm 2 sa dae
240 A pos tEdé O 2 ma
ooas or Erro CE noites Estale 2g85)
rm E! (quota fozam)= St st gm? p= 20,302 radio
27 2”
= 82. 20. - og
far) pe AfE dica TO Sama, O
º P=otoos 4
pão mara PIB redh
27 27
eso É -ZE. =0,47:
Perioo é Wee É E TE RP ade só 5
Zrosnss «
bias, AE VLAR VEDETY
a Cromnllirider) * ssano “os
uma a pes sore refinar) depot! Tired
39
:
Frame Pica 134Z, LAO):
IZ4S conTINVED or 7
E DR AE E1627)
t [0%+1] ”
é WE SEFk A Lécono VALUE Fo tem po teles
E8.9 Lo)
“é Ixsa) *+1]
Elaaeeto) 5 (6-ad)re co
eljgo- [ecos
For 3 merTICAL EIS
nem or mass dom
. alimt£o]
c-zé
E) susenceo ema jotoPomr qr Meo
E: mimpeJê
q é
W=m3 Je fntóo O
HEM E Male! -my(go)sino-Ta + (ma(B6)
motim spa= fomtã ES dem (Ga
=aE sro (fd, &
,-
Er im
EE as
o+5 1 o
ta q es
WE MTE THAT THIS ERUATIOS 15 ORM TIEAL Te
EQ!) OE PRETO). THUS INE MóRIM HAVE
F=2mho. tos Ly Feroz cd
NOTE: ThE Shraii ANSNER IS OETANEL “IM
RES la) amo lb) CECRUSE THE VERDA À 0E
THE WIRE TIEIRMALE IS TRE CANTER DE OSCE
CORRESPampINa TO THE MMDROMT E OF THE SIE,
tosco: né=L po L, Rcdete?
Go sed, brgede
(Ef. Frog 1338)
FOR A=0,3%
WE espere rar (neXB6)e À”
Sl ge
dg AVIS vz
MASI MOMADNT OF INECDA BBOUT E OF SI0E DIZ.
La Eles) mts Hb)"
=(38 4 50) eg met
BY SIMMETES WE HAVE THE SEE vatUE o
THE MONEY EE IMERTIA NBCUT E DF ERES BD ro RE |
THUS FOR INHOLE Wei JisueE
F=81 =3656 ade geme?
0) susto Feom ver res nes
“ASl page
1
Wamg = im &
EM El lep+ liao testo
-ms(É) sno= fm? E mt E
3 5, =/4 IS
=p se = (E ra)é
Lo B+ Eismo-o y
Fe SIMBL OSCILA TONS ENG ES
É Ê . -=EE
&+ s:0 - rias
e & E enã Samos dfa
19.46 |ya:
e minho
Td fm
EM, Mao:
«mf sro -myfsas=T tw ErlgtmaA
-“Pmplme O
-Imtmas TmfE
a+; + sue=o
PE EMALL OSCHUATIONS, SINO RE, WE LAVE
+22 o
& 7º
“7
2. 8 8 “ag
15 % CP
e =
º & f=5 DA -«
Poe f=a3ms p= 2 foiaostoa)a3) PE h0235 4d Ê
Leo Tircita)
37%
D00000000000000000000000000000000000000000000000
ma MASS OL EMtH GEM OR Lemero
T= Li? Po Lou Zm*
Lj me Lo atente) Eme
“ ALE tes
“= ê a-Lu- $E
DEM UM mg emo Lnri tuas
mo & me = En/ê sms +nféjis
Srlã-|me-o
[749] seom Sum or Prog 1233:
= er Fa
For Bop Sustenpep 47 À! T=087s Per
rima?
a8ys= zm|-*—E ,
7s 8 ra. (9
For ROD SUSPENDED AT 8! T=0Ns. fer,
a Êz
08 5» anpJido (2)
WE Aedo Emo THAT) Mdrga ORE m e)
ER qoa t (1º)
From fi): th = glam j
(x)
Ora ;z
27
Pesto eo gr
(a) sugrmerme (2) reom (1)
PADhs OF E yenzrs 2.
AN
na 72
DIM, ZM: mg E sina = (mp O)R + m BE
2. gr
| pr lsme-o
+R
For Smitt astrestems, SmOLO, we HAVE
2 sr 2 AP
Ho = À gr
e arpee TRE
COMpECTINE RD
SUSPENpRO. AT Rh: FT= 403 5
= 140 mm = O
ams . (0.6)? R*
h03 = 2 Eae e)
To a 2
(os Jr “eloeifo.mfioi) = Cos
z?
é = 0. 0M2/8 —o.0254 * a,onsg
27
=D. 77
P
2 ro 128% m
For Srantt OSCHtAHONS, SM OCS, WE Have m-ni= a(oncer no sas) te)
s+| 2 2,4
Sálo- o P 2
o Djwome (4) &y (8), memem ey mepogen s
Pe E. pm/Z -d (E)
/ VE = 5ae spo 2sar ra co dopyr,)
LATA: L=tr0fE
— Dn nn, = ns mn - OST
2(120 8) 2. a ó
20] 27.2 Mp MENOS T=imks 4 DERA ra = O M0W3
fp= Gerysa r, [Ég)
b a
[2.48] Comum Gimenm Peromus or Cores
B=iza8 mm
eszrruzns For rp From (E) mão (8).
Ma sasmess mari TR = ASIA ME (8840 É
els): e (DoPHSEO.ISS06m) ns PAP em
=2
(b) room dr): fosssos?aR = sosssosf SEL
E oornea- ao2vory = 0.004z
rooms Blind
1250
= 3
For Cirene Die Togo Redrt
Feom Sturm Or Pros 19:43:
= 27) e
Fá
(A) Poa Pabor
= am ..
(8) stcomp verve &, Fer same pero
birdrt mr a
= my Sata” 227
%-%' 2 35, 29 -
-
sedrô er.
3h “292
Pezr
adierto ars, Cen
gi Eritário
Cbamrldsancos. bar ar. BED.
PAST
ESTA Fa Ertemuera Das Togruma”
1 db Atgpro
? |d=P Fizom Soruvzos ve Prom (2.48
el ã
r 7a am| Dt Tod
7=2/ 33 «
lb) gecono vacve, do, FOR Spme Perno
feto (1253
(0) SMALL AscuEBTONS ABOUT VERTICAL AS
f Ze
EM FE atE O)
Ev7 we Nos THA
Fa HoBtZona Compre or
TENSIO Tm TAS WE
e EE
Zrr p
mega a EEE = 27 a
* Let)
pis tr iso -(a8s
% 74 «str z z ,
ml =. GALO =s é x
3 dr 49 7 HH, 263 500
2.4 Lp* era e
Sirgrátgr =0 x Eh
Tu: Sé
fo
Cerri ércos der on
bg rd
18.54
+) EM = EM
=k8- Fa-iê -Ko-E6
«() &+ fe 2-0 h
PE 7 +
fi o melE w
Far Soc Dioreria SPUERE Eos»
Te Zmra 2 o.
Lo Por Zgrrpr- grep
= En(one)S Crato fa fa) = 128.48 315 “fg*
remos ff do «4
6) smp ascnentimes mm retas tttne
Sove Em) sor Es PHOSS pão 2 «q
E 2. R
J= gps 7 5 z BR (2) Joss | Dara: h=03m d=otm, Ls odm
A ata mréers, ma2 04h Pe ass A
Fest ovmrs re ros 4
= SE - =E(m
I ec ssmE ensaia “bg m?) 7 se * Tm Eles
- 1 . ns
Jos Store Stgem az fa-1ê ôrfe-o
- = K
a Le. SEDA EStgm? + e S pa JT ()
RM 0.45 & id ——
Ko 2 1a Faz (2)
fe p= irasrx tm? DB: K=195 Momfrad
- 3 m= Ag
p= MID3 Mô em os « 22mp à S/249(05m) E2saD “da. a
= MIT am
“e LES n107E Áêg vm
(cet) al a Ta Jizis A
tconrnveo
3%
DO00000000000000000000C00000000004000000000000000U
0000000000000000000000000000000000000000000000000
i
BET.
O) Cscueamons 180 HE PMMA OE THE HICOR
5 2
framr
EMT Ma E
—anstr ciroj= Ta + bm, Jr
. qu a
can des = ar Êta E
S
= - fã /
La f=a5 a «|
$) OSCHLA TOME 1 DIRECTO L PO MOO
a eri= rê
Ea Ho)
E 2
607 Poe suo: domo ls EMI EM)
Ig 6 [17.66 Im SCI TONS Soo Pein oe gieie
â
h=€ (1- “os Sw)
h 6 Mm h= tee;
canm Se Ea“ Com
irfme!
Pespow |: T=0, W= mgh= Lugar
Peserras Rº VorO, Te LIMA + Emi
Hime ua foco E
CONSPEIDOS OE ines 5
Wrycrm: O +fmgeéne = mes um
BU7 FOR SAM : Are çom imegtz Em tes 2)? |
2. =
fs f- 5 fã Zi 5 «
(b) arvtctrama OSCULLATINS IN DIRECHOM PERPODIIMAR TO DIS,
h=e(i-cos Sa)
= 3 Yo
Wemg
PIAMESaa
h= É 0a
HO, VEmgh-dmged
nO Erflartm
= Mime Junio denlerm)= Emciuê
CDA VA TRAMA ME EPE RRS
DHUmrm: orfmeaio É mewa
2z2
z A
Vop= tus,
I=z
Pesq 1º
Vesrrrom 24
-£3 =.
"Fê ex fez És «
132 Mm, PM? -oglreins; = Jortwadr 7EE7
-myrmeo Gar Era E -
Ba Ss =
Sri fjsme-o res rastt
Fem mal? escidiadra:, sing me, we hovs
a W/=m9 od da Th,
Z Jo-o pão: É
, É h=r(-coe8,)=r(Zeê) a
.-& ta « Pesrruw 1 qro, = Whk= Sogra
may 2: Voo .
%E ETwprt mr) Hirmrjug
Cos; ER nato DE LEMBRA Y = 2 J%
Fry =mrva: O sfngrei= Hm Dom
Be7 FOR SIM: bp By
dmgrepo Te arhes) pt 78820
mr: Ene a r=3H, “ar
4 ENEM
“o ty: ()= SE
Tello
T+ de SO E Zegar= apr
T=222 6
399
mm
19.68
19.69 contunven
+
12.56,
ros Hs atom A
tihe), |
Leostm A
mm
L c 8 N E
mp
“E
+
Me my
ConcERVATOY OF Pa :
FB rves or dbBrA) Edo foot um
BUT FOR esto, tur 8, Hrbra dao ft tro) |
= EMA tA) t9
NOTE: RESULT US MMEFLENORNT OF LENETH OR 50
Wey =
E odm DA zm:
. ) Uta, Rr Slhjn= SE dote, RES lj, = 60/08.
Pol, fu, cm io La dog? 2% nad seguro
= mas
+ Ec APR + s0 tora)
Bsgm /: Teo, pen feas,-mtcoça Porte, Nsormgm),
Poseram Memf Castor dast p= asas reto (= BRR qu530 0:46
Z=- 2 tz Emas * Pour Eri VOTO | SEE Serra cru R$ Bor Deepane Sr
Cal mem +Lu£ nei EM Jg d Lt"
COMSERVATIAM CF EmsREy
Zu = +Va
O-Emteasm *" Lt iu
Emat(i-costa)=
Fer Siro OSCHLATIONS,
- mel
Sed et
O cos Bajo ES
pr E Z& 2) tn
Dara
W= 64, Bo Sola 60 bt, = 3a ==b alt,
tod É 4 “) = Sai
* “les te) (
pres rp frÊs
197
Fa 4564 «af
SINCE VWigipTiSm TERES FLS (GOT TIE
Fesp or Ds
SLIM EL ONA TOS
=?
Ya” 7 Em
RA Em
Fosmon |: F=O
Ate nietarit Aldo et Rb)
214, +) 4 Es
pera Vozo
ms A tie fm ze = Sn u + bol)
+ Pu
far f 2 Em lconnmuzo)
417 rt (e rm!
ml Em e San ug . POSTO Cr LEiUiL BRA, WE SOMEL MEGLEE
BUT FOR SAMA, Cy Om? Fm Leo Sntipa) BERECT CE THE WET ANO TRE SEAT Eis: o
Dt
PEL LL Es o of
27 - =m|-£S 1 a tm
t = f a me 4 A fam TE
" Set) E
1267 À sim VIBRATIOO TRES PhCE Mgo07 TuE l. 8 tm Tg OR rg
Posj Tom Cf E DUILIBRIUA, ME SAB MEGLECO TIE
EFFECT CF THE WrttseT ANE THE IADE Dirie crise, E OM Om” SPRING Eloripnom
Dist: m= Et, LE Linho j= 005% Bm
5 e z
200! m= SP, Log Elos) = extopi) Bg-m
a
ZA ÉS,
he TA =
L Limit Elos tm
Pm
Posrram |: Ze. A (stay =
Psi 7 Wo,
7 é nos) us elo toaruçr foras, = =0.8
CONDE Tra QE ENRREY
Drh=Rrk: Oy214bg0% x O Bs
BUT, Por sura: temo pm! RAVE RO = CRM é
rim
p= cegos A to
For = «OVA USD) LEAL
pr Eró7E medir
7 E -S Pelos A
1972 | ser sozuTis or Pesa 8) For Deer or
Ze crozoas R (u
LA
For Pejás: EE; pe PRE
R-S08 jm
EEf orosoua À
00
1000000000 0000000000000000000 1000000000 0000000000
q “o
NÃ LENDA»
e (CETTE Ca ===
lu NE da
Tn MMS SPINA DE 06 Mapas
Por)! HO, v=-78 nã
Feet! rem Pos?! YO, ze ratio o |
Veg * Dep" Rom DOS! TS 2 Z- Ee ks 7 7
Ze É
Bs f: tem Lérerero) Vetoery = O o= €%a + (Em, ue am,
n.º = wfl-cos,)rwfli-cosza,
7; drug essa) mdl) e) 7a Lona t 3 mao SE
a Wi [! G-daz) +10 200.99]
g CONSEEVATIN OE LEBRE
bofntss Fry ema: orBu= Hmgs 3m, ne) Um
, 2
bei dem moer) ns Bum fest, pras Anão Elmer oa pda)
= La de rá dem + ando ri los 4 er
z : RESULT 4s
ciglte, tz a se Tag $a Do ImoRtenDEN? OE
tw
44 IL) ME EA Hom)” .
15té À ê DATA: La LBmm, Mar PR Poe SA
Wo
2. Soon = 13,408 vas
Lu ai = Et ruiro + Tre salé é 185.85 p= 16 br
? A º ) 12.408
wie o LE ES feziria 4
Ewfejo LE ” 27 27
SET 20 pi f nºs 3 4 5 5
E + E. anjo, (376 | Besrrun(ã Bis perl
me e 2 $ mem, «(ETR
MeTE: THIS PE noso THE PEROP OF A SINGLE HeOD 4 e Vis Da
19,7% " ao Ty dE
For Me, ã j
Bsrpem (1) Cosa core BisJtos Say
komempres uz riam = CÉ tura 2 fire Zara
2 a» Lito, Ho EB
Yam = E C)titem Etr uça RO
Pesrgr É: (ram OISRAC ELST)
POR iciricompaey rt
ses Ata a TO V-Hulkaleca, =-S im ccô,
Posrmen 2! Crer, vececrry)
2 = Tio 4 É ren do | boa TA o
Fesmow ! (mas. Ger ecnor) A 2[$ auto me | z : va ia :
T 7-0 = wéli-cocs,) +WÉ(i-cos 264) 2h So)r ar t+ + Lina)
swf lose te) +) ]
: - : 48) ri -l-átoaJ) == 22n8 tm 3 hz Us E) é tu
VE FNE , a
Posrmor 2 (tau veocrr) Wi s Tebrgrh: OS ha 2200 ÇE =| bas
come arm Pena JOE qr ig hem Vara acre LP Ebidi-coss)
8 q =3
FM =E+Vg orFmei-fitugeo Bor; I-cosrnisi “ro Magr 40d
2
2 A ALL
cera isto: uteis FEL apo a 20ns Sir Hogté sã)
= Ze .
PE ZE rt «(TU sra gestos
” Ea 2. Leedlzza) = s:722
POE tra SEDE PE santa md
fã EE cogors! fomi 4
o
P9.BF[Mole: Fw av bocy moving m an vdeal. Floid Loves) % BART
there is no fréchos drag, Thus, this nmolton . = It)?
x not a damped vibrativn, However, the kinetic 4
eneray ae vire by the Flud myst be included =. = -
ia Ta sofotium, Bor a aphere FNE ME, já LEVV3, Por ond o heiztnto, Proto
Te) Pasitim é (Mox, detlection); E Firm = 9 radis
T=0 VEskzm P=A, sa at - >
| É=Pm Bolo = Sá =% x
Met (ax, velocity): Vzo fa Em Sie nb
Te Tie hM AL PA (0) was vady
Fem Taio E EM Mig PV Um x teres» premio nao 633% AQ
Trb=heh: sho -sfmegev)a Mojo Sea)”
Setting Ela! shaum =E lim LEVIgi A (6) w=42 rir
Pet Bot b=3 Mi aaa mera tim 3 -
+ Emo FEV aid Aê ima ur É a] srs Em SIS am É
1eV= pefgm)=Enpe= pts) = onssve four or tuas,
f'caasbésamaa” 28) , pe itoz, TeB = Oares 19.87]
(b) Accel, changes apare! 'weziris! but rol mecrec: TEOSZAS «|
19.85 Edo A (Bm a HB,
BorD as asraç
o E Mons) Fra
” Static deiinctm =, =
gui rebegrzdreg | a
Tuas, fem Pe (14,83), we write.
tm Bl o teto br
rirrrrremeerrereoentem lie Cena?
ra Em (Deum
Posso (E) whor O=O A,
Brdor so Mar, deblecte
We rent E | >5
Er
Thy, me must have
Z7=o V=Wyg= mmaÊ NS) raras
Peaton 2º Mou veloery
Ta Lic En Dj Yo Sine po $;
Cio € (2a
BHYEDAVa Or Zama rede tom É Zm ho
Seldoma temas Ego i -
7 Somrefegmtços [19.88 | e solubom of Prob. 19,87 for derivahor
Em ço! €)
” ————
ta E TE
We most E e] This oeurs IÊ
eilter Cet >), whith means fico imposobla)
dj Ile wriich meses (n/a so
Sa “E a 2k
inte + a E «dl
sor
12.92 fo) rom siena comparo: ReGE Rmtm
de Cota
dm si E
miar oe > E>)
É me [> ff!
2> — Cá >0
MATRA FrEGUBMES CRESC a)
ejê [EB = 24203 mio
fe Go BL armme= 20287 qm
(8) mes roma R$ EPE vais
Fãs «ad
Em = raf= “non tfi tetas DA s2N
Ee PESIM con 7uo m
TS Rbifm
270
FER WE PRO ,M, With prtermm 5 Soma" Er
Po fe S00.27x15 Sm, é
RI Lg7 EE” =- 98044
fartas toj (GF a A38559)* o
= 84% «4
(007 08 Paase)
19. 23 SINCE AMLITORE DECEERE] CONTINVOLSES,
2
fo ai lrposciesr)
[1790 | pres
Em
Foo d-fedaj?
re cases | + >2 or Ida <% or - cê
2
Ílrees, toe cmmçl da ci -$< De; < ;
J z
PO MA) <a
a
4 Va<vlg a
CT] fi Sum comeram: per GERA AS!
. MAZueA, FREE (e son ae)
Tele EA, = ares mb
+= Doo CT ves dot tm Letivo |
Cb) ez 720 rpm = 26,298 mdls
WE NOTE THST Up. WE ssume THAZ
VIERATIA) 5 FOR EY A FIBES Mm LotAns AT R
Dime E FROM IHE MIS OS RETA
£
Ferro Focer a Pas mew”
EGUPRI; For rp mit) 2
BaIE eretajoi o = Lia)
A ? Cfr
EUPRESCI ME ESTA CO AD qo ie mp, E Te
FOR = 30 nem, EinpE PETS da,
ag q (UA fee mo
EP [O]
For dv= puro, Copo Oro to in,
coro o O ajlirco CT
17 CE paogiz (2)
el!
Ovi ER) 8Y Edta):
2
com (mor (tes
dor — fre (E=4
geo 1=03 fe ser,
Á ligo -0.3/400) “e
Mute?
a
=0"7 p= so XI eo)
LE amo nl ras Pote agfosembe isso mi) = =RSRM Pp A
Em RRSIRM
Fa LAN
REAR buf” VARA “m
For 02 720 tpm, cdk 0403 tpm: S= demoras
Polk Jpe2205 tm 4
HeÍtR e da 0% Pe fiagas O SED 246 o
mi SAD
fovr or fase)
405
SAE Fe ESTATE MACUINKEY, see “Pesa 1êra
17% continveo
WE Me Foro: PE fake
x, = Lt)io ot
* ()1
WE sháit EXPRESS BOTH O Aro O 1 rpm
For tu * Boop,
Fo AM UNBALONCED ROTOR OF MAS Pe = ls,
FomiZNE AT dm 1200 rpm m LREdspradho tt
THE MINSS CENTER ATA BisTâMiCE V rom
THE Axif OF ROTRIHOA, WE HAVE.
a 2
PE Mato
ta cond) ae Cgi (à
for los Gn, 2m,
mp7 DO O d,5 Ea dO qe io (2)
Fer vu,
"E DR Gg2S = Lt) ae (cut
Coats
Divgê Lott) &y Eala) ano
SDLVE For p AS Boné im dizos 1798: po = 255 pn
Diwor eat) ar cola:
dos Ea
“ORS - ef. (a É
(Be) -/
«SOLVE Fole bo: v=27p7m «a
1795
m= 88
Four Semp
EMI OF Consta
e “O BNta
VIE VETA E FEI
WE MO THET MOTIE 1S ConSTRMNED TO
MGUÊ VERTICANY.
a sto ) = Meo esfm
= 160 x40*,
pl «| Ei = 7828) Pdf — P00mm
Fere ty 1806 nm = RSS md WE GRAVE
Dee LS = AS mb?
- , «Falk,
eatirasp Em LOG
ms: Bo ray vê
EU]
3
= lts ua él (e) | = "4/6080 om
four or pysce)
Pas (io animictseda) - d86% M
leomamoro)
Bm 1BbYN cut
ee =] XIO com
Tmguz TO fg Poliasatado 26
= 2%mm A
. 26
; FÊ From BooB 192957
pr PHIB] radio = F00 rom
For UNEALANCED RODES
=,z
Bp= TRT ts
FRiIs o rrecos:
£ bene vejo? - (08 +) +, A
7 a 1%) Tra
BUT FOR dz 1200 rpm, Dor 4S wo, Pre p= Dão
-53
-a.ésénio m
THE MEGATIVE SIM IMQUATES THAT Be Amp Em
ARE OUT OF PARE, SUBSTITUTA tre):
EE coessuim) Lorca)
1 ooo)?
(0) For az GEO mm:
z
“asa
x = (0.682 116 m) Poa) 1 0.296 m
- 1 na)
Ts DP gm E)
Cure tras)
(8) Eee w= 1600 pm
16
o9E (0-6 std tm) Lapa = "AMO NO
1 o)?
RE HO AO «4
(our or Prásge)
(x) For do = 300 mm
z
RF loser Do) Leal»
= .
“Pool Lyz SO «q
(Resomes )
406
roenessettatttttecteaoetetocttecececestsescseasem
E E Force ei unbalanred retatimy mochinera Ad = fEOM doom? h/a
AG - Za Era fa=mãs meu ado 600e8hfm = 2g0o
É P= sinal mo RR
E pr ISA redi= 111% nm
E no Z,= =(2É pj Le (1) | (6) Resonance occor; water
$ = Eb 16 == 18799 tpm - «
+ = qa E tray tp us lanr apo
Hhen ob jret loses Contoct with the becm p the maximum | (b) Fop = 130 %,pm Amp E=ABma
atteteratica of lhe bema ds Q,= nd, since USE FavADOS PUB/VED 171 Pros "Eroz:
. . a” E 2
AE Em 5 ds prime, defechim (5 re el, e fo2m (ep)
Zn= E e ra é
” a 1) (paso pre
Ta a=6), = 800rpm, we háve ZmD6 andãs =2, “o72p 17% |
Senti nar o: ; “e r=09%wmm 4
£ EJA NIGO/ A ()
Beber) mo 210%
ro eim ta J200 rpm, ne have 2, 0 One nd LT ea dmisto vê
Sutstoluting im a ant — Spa
de 133 |
— a '» fas ag
g ups Ts” j 4 1º %
i
Didi Chi by (Dmex ver by members ;
” ma, 1 x 0.&m
E (5) =
4 Fe
Y z fas
( a o 1)
E) ENT = E) Frow ERES)
and, Sinte auf * =2: :
3” un 47 :
144 s-8) = 45
is * é (7 mit Ema Omm at Zy = 3am , we have
e... ' o = 7
de 49 [53 cltoomo) FS f=éstpr A) ago = to sec tal
OA ta Pol
DOI came E descreo à ereto al radivc Ba, tir simple pendolem; qui £ Thus
tre:
As (nre)w” w* =E( (1t3)
Since the deflectin of Je Shett dg &, the ade
teme exerted o dis dk is . First solytimo! ur Etud)= 4% &=5 fre
F-ka
Ea = 2 ED
F=mã: Lt=mfiteo = 16.380 fal = 0425 ficgj= 2.64% Head
o E .
But p=á. Thur; f"= tie as” MM =8I7S, vd, =2857
x — — -
tp = tu" seu
, 2 = gue
Ber
4a CC
CP (RED)
12105 | uceto 22) Bm,
ERG 83) x,
12/06 FRAtaR NAS Doro SEDES,
om 0%)?
Lee À= 600 mm, Lm=2Ndm
For E 400 mm, Keys 35 mm
9. 2%
= ande” =2p525 PELISA radf
cole): +3Smm= (2)
Bm
2
(55)
Pod seria constar
Re 2700 tfin)= 200 dófim,
B = mo dó/re
Wy= 600 16
2 8 Revolatre
ES —— = JE88
fm 600)» ama)
p= n247 radk
(O) SINCE ONE Compera excer Or THE
foMp PROFILE cortes! To A epieTa
OE SAFE, TUÉ botoes Vo AT Resomper
MUST SE SUCH THAT JHE TEMER TIVE
(E É dm ore eve tab
, - 27
CHER + SIM IrreRDES PAGTO 15 “pe pose! = Hp
ARO — SIEM INEIORTES ptb Trois 13 uz ore Parse” ru LP DL LEXL ara) 4
ASSUME pão Tras 15 “UM AAMASE ao Qruoe (1) arêo) nn SE = (M6) 55 = PALIO = 287 fes
2
se IO GEMAS ih Mr 1870 mia
se a (8) Potim! THAT W 15 Bofmer MAL Ta 4, vê
Ainve fere T= 40 mifh fama dm LuSpm *
Fe 2 (66) = 3s— ar(aõess FASE ) Sm Sm Sim, ,
Hs T/3 O gas To Stem
«oiee eee |e tt WE Go
Wrses)? troyss) «
Um = CEB ig,
uk ten = nrsan)=m (bum o As
2 L
-— IPO ESIBLE — ASSINAPTIOS TR
“e te OTIS 45 “um BASE” US f2107 Ser She; (a) or Prog 17/06 soe
Ne7 Coteladcr
WE Meo ATOM TH8T Ator 1507 or eus
Dyeis (3) ar(z)
z
2. 1 Go)
z
1 (567)
wa a
=20+28 (gerar) = 35-38)
aj ao Es]
“ [dE 5Ê 7
COM PUTA TIO OE Vecaciry % AT RESoMaNcE,
A= 19,705 milh
Ervas: Anahi,
zoist Jar
am
La DS a,
=
Snes | AmfBol<, WE er mae ap (Faces)
AMO Up O, WE ALSO NOTE THHBT AS tus,
tus
x
satizaa) —- Ls ! =
(usem samsoa)= 59 de IAG IA)?
toÊs 40,38 caça —t—
Bj?
tom ksIpy mdf eae hr -« : f á
[BC =
SVESPTUA ro Ea): 1=(haj=-2 (E) 3
E
Zum =
- FAIA z
, case)
Sartre tod Te-steme
Sape SIR dem 4
(cuz or exase)
VU = (930 mANE =2%)8 mil,
vEPH/mih
FOR AMY SPD DS BH) milh, THE MARITUOS Egg
DF HE TREMER IS LBRBER Tybo MIGA, faol2
Siro mEpR BEBO Us, 1SO da,
go
oi
57 iôs Since re me vã EA ra), where
A<O, M<0 +
At
. x= pe?é +Re €1)
ars dE = Ad) ts pa et (8)
ta) 20% 400 Eys O) oral (2) piel
Mm: A+8 0 = A+ BA:
Sricg fe And E!
2 MH x
= gos = + *,
-2 Arrd
28 a Port E into(t):
e E
et ge 24)
Tur pro pher ffoe, mr ml have
2 4 «af
Act geo 2 2 O) (3)
,
bi pel cla? PdO, Da 08, Chonsime Ay ave By
Btito ACM LD ye how
pe 41 ado Gr dpdO
dotar Fo der 4 (O) cuamal
exist, Sente remure Gate rorgal fo
a donsitvr pnutr be
Te xt corre du toe
A
6—>>>—>—> = é
B + Fai O oed CP) greid
5a
cosmo!
()t=0,
PMB 2 AD, +82
Sobriny fm Mar Bo
- 4 Be Ln
To dah dA:
Suiet teta da foot E impoli):
po [et mt
Hz 2-3, le ]
Ta z=o who fico, me mut have
Mt cent
Bi, freze; AjÉO Thos, no
Com avist for EF, card He bodes mil! neve pass
Eh errgh jte postar of es uilibrivm
Lolotrom
The gt ciirõe fr des
We substihde he inifiol cmeibime 2)
19.109
fes Thom E, whror is impossible,
f=0 ,2=% , V=y in Bs)
ard 2)! Er. 19108 -
Z-A+B = AM +BA
Solring fr Rand Bs
f=- Mo ão Be dedão
Arão da
Subsiitviry Be fand into (1):
at Art
xe Tam - Mae E (og -Asoé À 3
ra +
Fm a=0 when Co, we muit have
E E
Co Oje lt to Amo )e
pPacat = Mo Mo
—2,ão
t=—
En Yecnão
Brrdy
o" di
This defines que solution enty. Ausuminy Aenco,
he mode dee! dois Lolyhica
wlo ef E Mo
Pajorel eo ja positive Fo AM
* att >]
fa Aro
e ra check hat +his il secor if eo
Ton Shpe= Ae
E.
I9.H0] Fr tioat Mampina; C des
Ene) x ge sin (gt+t)
AE given max atplace met, Feto, My
snfgt+b)= a!, o Xy, e tm
AE next mor duplocemens, tc, 2=%,:
sn tatb=, x =x e êmtm
DD
Ratio of Juceestve isplacemen ds:
mer cc Bt) set
Tomo dm 6a
Thos; ln dm. = 27 e q).
Zu mg
But, From . Ep, (18 4Dara (ta vode
PAO é
Ele RED)
SH
“=800 em = 83778 nadis
URGALANCED FoscE à
w=/o2= ke 6,
= Ê Z
Fm 'ro mana (E Nosma) = see do
(2) Mo Doropre :
SETE
a
- «oO MIT
Ep ré Bam JE” oooas fi
R Jm Bars,
Pesa = em
(rg 23)
Cou7 or fase )
(6) gaapeo voos, Leitos)
a A
Hg os 2]
SEVEL
7080
[8228 fe feto cosmo
Komp = 0004983 EA x
PURSE PELE PoBY RE Poor Fem Latrês). ban ChSH)
Em” O h0B4 mr, «q
us DOS in
LEREM! ms
ITHP creme Sorrstairs PBIRI | ros Bavrim or Pos 1335 me gia
Bs SM. sp2z = 7000 loft A = 1€0-emfm om= 189
E” cosa, ” 9º PERB red) 200 mom
ETA 2 ' = e.
E Vigo es. em) = BEXOradh EQlrrr) mm paz(nirm) = 339% M5/m
FOR exe rzopm = (P$464 red
% =4Smm = 4$ x10 07
Pla
as 350 Mis)»
2/280 Y 428, sés )
|- p Les ee E ao vs
CPE ze) Ze, 2(F397 PA a)
Bla <a
f (07765) eloa)? CEL
Bot (EZBstao Niton sda 527 m
pai =
Lo euasspuo”?
R
For Foror cre mass m'= HRg Ano w=/ZEssy ras
Fo 4909 M
Pur (gy lafrasisir ras)?
F= 2/3 16 /om F=2/3 pm É
Poa? Pe
/
1740] p= sr000 by )= soco dóliz. = Heoco trt
= LS000 4
Piá ee o)
minosalha do, Po ft
des SO gom = 158, POL radfo
Bzmputo mes (Epa. JE covas
(a) no peer: Lepr23)
8. TIE
ph.
$E000 Jeff
E
“Entao da
0) Diem: Sonoras sro(1982)
fm, e
= /25. 7/8 mdf
Une Fores:
="cooral FE
four af russo)
= um to go e
“O sasva Êo O Pass DE
(122277: o col 2226)
Coy OorçÃo
Prese prasze MY RE Foo PRM Fo fred), Po Eai (1999)
Hm OOPS dm. «q
a obeso A
Elias a)
P/20] 4 É = LSetabritnt) e spo Mm
[E ELI Ku
+ VE [2222 ar = SO. 425 rede
UremAnesD nloco meidhg = Oba, Fa Mma=o.07rm
USE von = BEE md
Bom'pule (04 Bafo 0rsm)l 4,28% malte)
Br 13d60 M
Ema
COGU Cj 08 mm = 85 tm
“3.140 M
oB ui? = — RED RI NT
H-cesoe es
spivê coa É -00mMS o.og8s «
<
< Er
< o
(8) calrmro): ecutmpr af afmnso mad )
CO GOLZE mesjm
Form fez (o):
m
= =g.a7ov7s € eloofoms) ova. 88e fam )
= 658 4sfm
O = 366 Mm
Ss
DO0000000000000000000000000000000000000000000000
12.423 | b= 2 [H8 Rm) = 96x Nh
A =[E - - E = 285% radh
sc £- Ea = 2205 H3
G- ama =2 (so se)» BBEL MS
z, = R/% - c)
Ei
f f gs
We have
o 2H = 1088
Ê ” 2.205 H%
e- 1600 Miss
= Lego!
E
Trento
Sobe totrç into (1) with Balsom we have
=Onsty
19.185 contimveD
FOR ANIMA AMPUTOOE. VE
Bone cre fo-siomalp nto moreketcs r-dh)
MRE SWi veda = ASUBHa tos 278 vm
te) Ameuzuçe EA :
sEDUII, 82): Zmã .
2lz E qr
[Tess
Eco mento) port PaviPSio ro mag
IES
= feto cobras tr Laos A
” fi-Fpozmao -
For art) mera EINS bro Prue
sed
Yz Soso trfiy —"——— = aos
use qe ensur OBM Im Peo8. 19417
(fer ae feratorrma)'= agrss
"H i-reg [torres fonena)]f
1SON/ 9681 Ufa mr Oss A
” “Tr Cronos [etotencam IV IZE | (a) mo Dameme. sms as Pros [2/25
Asg2SKIO tm - = COCO ME, po3n08 mp E=297pm «q
- ge = sozn46'm (b) nsgbeo Mao TISO, ee 12 los = [5 dons
X = SOR «q
Sobstitulms fhe valves found im Ss
IUZg
Prob. 19.23, foge ther with 25 = & xrom
po Eq) Enh I9lzs,we have;
mui MEN f 26000 if
/ ines PE + E E (108) 085) ]
Solum fa 2, we find = 0,/58%
É
Sim q =/3854xm Mis, ue have
€ = (oNss [IS BSENIO Wise) = 2.19 210 sf
C= 219 ANS
(a) No Damme
B- acena ) = Eco db = S000 IB fFE
12.425
-| Ee = 3408 vodf = 947 bo
? YE Cocibfaza ao
Poaifansaã) fe zm
fá '&) DAMA MO TIO
0 = Pubs) = 108 lbs/6k
e 2mpe Alec 3408 red) = SU4.09 esa
E. LO8 dose .
E Pucoguei * ANIS
(Eomanvco)
Cectmp — EUA? dest Lontra ps tn PROG RI25)
D-! tosta
Ce gases
FOR Animais AMA RLITUÇE
DETApED 110 Frog IRH7.
(igor def ao sra) oxamo
w=(o srs =(L0p28)(3108 resto)
w= RAMOS dh =Rz025 ma m=AsR pm 6
=0, 37297
WE USE THE fRésKT
tasas
?
Cc) arserpor B, fa
asa): CORTE Sr
EQUIEI) Ts
fre Porrla) vara PE tZSho ay tu=p
“RE
mu, food cor
” [E-Fefposmmof Cmt OFBSia.,
Poe PreTLO) vira Bxl2Cio, no presa
tas tê
== —
Km5 0.030) Fé
%5 0.36) tec,
45
*|9,127 continvesl
+ FÊ e so
mao
Ser = (At2-3)
1
mr ABr de
Leco car We RS, we were
a
dê
+re = amas
m É cgtrkr e Aórcgê 2)
Morar om mussi (5 sine cover. De Bm ut
SME SSLID 45 U INTERVAL OM TIME REGOEA
zo reuse meme é 13º te
GT PMEND DE MOMO JURINCE 45 d, ThE
wb=27 wÉ=m er cos Eu «4
Sogsmrwzma Sem Sio mê nro 0) me meme
-«
“7 É +e É rlz = (Rsirat reto cos vt),
(8) aueerrrone: covsoue SEPARITEIY THE uva
aee
re rd AS, om ut
PMES CGUATRO AS SME AS dK 19 V6, EXCL MT Paled.
AGU SObUTIOM OE FORA
== 4, solve -4)
AND SROCIDE AS AS DONG dit ERS 2SP ToQOIA 175%
WE Fomo
=
O Nek camas Gcm)?
como ses
ms ne Bsdr= = cuba casut
PECALINE TRA Cos wê =
am E
O qe
Sinlmbr 3) we sv
+0 & + Axe = 10405, sin (mé vs0)
FMs EdUMTrO 4$ Mom SANLAR To dO IE, WE Assu
Sotprmm OF FeRes
x=x dofutom- 4)
ANO PROCKID RS dot EMS JHLD THOM IPS WE dona
x. co sm
2 YR mu (cw)
MRE SOEVTIOME FOR THE TWO TEEMS, WE Move
X= x, sofwé- 0) + Ra sin (it as)
Rôm Sinfiwt — 4) + ve tu Bom SN tr 30" 9)
VER mas) + (cut
CoNTNDER
(3
TERMS CE THE RMNTHINO SIDE CM EIEER EMAIL EGUATIA]
WE SMBEL TEEM THE MIAMI) VALUE OR
rus musanearor OF cQuaran (2), de
AS Sin (in +48) + mu Sam So (ur 2)
Consoante TRESE Pwo FARS AS IME VEtTRAE
PROJECTOS OE ROTATIME VECTORS OF MIREMITUDE
Rôm ONO dt Bm,
MIRINS VOLUIE QE MUMECSTOR = OA
082 VBA (cuia)A = Su) Pecas
TOS ComSIDERINE BOTH NOMEESTIR ANO DENONNMATOR,
WE Mare
O e rd IA Sm «
me) WB lou)" + (em)*
“19.128
o 38%,
o =
Eqviesêenm
Postes
A em ) 2 Brg x)
Tela - Ag %a)
E
PE, sinwê
SINCE THE CRIGIMS OF COMDINATE RE Eros
47 THE POSTAMS OF FOUILIBRINM, WE day GMT
THE JT SPRIMA TEMSIOMS QUE THE PFERET QE
ERAVTY,
For temo À:
a ZFemas Shy +28 bt) e ig aj" a
de
OR tofo E:
- 2,
+ Ema: 6 D sinat -PRfto “e (do tj” El
PEneeaMsme “ES M) Ano (2), WE PINDS
mk, ER KA Aria) O
mia 2 RV TRL +c(%- daelsintol
é
HI 6
JS 137 coxrórceo
(b) Fon q xo.
PEncrior ATA 13 VERTICAL
(EM lMe o: Wibsma-Tê
-myilsmoe EurE
te smono: gs +8E80
4 E -[
PE ar Ze 27 F «q
17.138 5 Et
%+ Arm fofas e bas
(sca)s o
x
- Egeu
(no teme)
oo bo)3
(2) pieema Fist Tuo SRETOVES, WE fava
Eru £s0 3 == 403
gmus: > A %yz 1004 = 98! NM
guor R= Zoo RNm
(r00 rim tea, PEN
Cy HAS tap EV mem 4
/* E dedo « 1333 pr SEstralh
fab el gt f=ctr «q
GB p= (PIS mass nah) Cr /TBlmal M
(8) From cam stezem
Tn” e Cm Og /003= Soy = Sol)
ar A A
pls dass miti0085)
= LOM nad
= 428º
Usina THE AunIIMeY CLRCLE, Wo
Presecr Va db THE VEETEA
Ms
Se msm pls Crrventilnior
UR /SRZ male +
(e) For É=002s:
IRIS] weo ADA = Sob
com 800 nom n1885 radir
mm IS vA.
JE [Fes 170.288 va dis
Ad (6m)Jra0. 20) d ”
5.
Let 19. 38) Po fa
>
oo Seo = dm
OSSio = Ram) "SAS
(E eg) .
mz -A0 7% vi. daz 4077 mm, «4
Cou7 or ease
19.140 ie A E
=) =
A TR ui miami
Mito Lya
DT (dp AME +T)ngo Mar(É + 2)ma
HER Mari rejngago Mel 3)»
Za? E sam AE mg
Basa ME Jma
SEG Hed! far fr om
«mpg mê
Ertdfz-o
22 E. LjZas
75 áçha tás 4
19.18 (0) + 2F0 mo,
q -mg Sino = mãe
R E A Eur sis x tn =
Tiyemg
o =. xr z zo
ug: e 3 2”
3
Cora frgum, utTs EG (PIB), WE concLvoE Tg THE
PetD CE DSCHLATHA 15 THAT OF A Sinafes
PExQuiU df Leme hz R (BED)
(8) qm 54 unia, = ———
F=an|2 « Fe -
2: 3 =27 2.8 mdeo sosz s
OR USCUSTonçor unm
reamfã= af xcecijo = S083s
DE Bt am
Flo Ecttenm):
bm. =| Ea 2 =[52
“eta are e se q as suo
27R - E mAMTA, ED,
qm - 20E a,
Pena VaR 2
= q an £
P
HP
IP 42
: 2) CR
=
Pe Coma 08 wire: e D4O lb-in. fml
Tróia
ea 15 R, que Resmove THE
» ao EPE ATO TO
[7a 7 De Rem
e
a E
du, +
pç
= CÊ do-ftfrad
z tm gos |: (tape gre), 70
- = Ater
+Dzmpa Elma: Es E Porn RE (mas. ii VsO
ok E = fist is [Ho Eds 15) su
treco Con sstaTor dE LHELEY
20x zm “Grey k rm: ordni=Zaiio
fas z "a SETONE Vm 7 pum AO An 300 Mm
Fon rs os am kz SS tb-fifmd É Bce)ra= 22 dota)” as
- pasmo pano robo Isa
30% = 27 roxo tes -
Weiurs W= by .
Pod) nobres LE 2 IRIGE | me maes Co= 400 np pu (Sbnfso) = 300 tpm
sra Suck er Ada TioM 15 CUT OE LUME Mp0,
a o » 5, à
p= . . ; EMtIRIE): —Yyz «es em Sm
R = 0.sm7 Lo zat dBstr mo go 4
19.143 Saraos E SA pe E (1
pis = SR
Fosrmo / + luas, DEP eTRA) Gro
TREZE (Sra) 4 Ed
Poema Pr (Mana, veco cr Tr) W=0
Ter iistoa rat a) Balas H5D) |e pare
consmzor cr Eptmesy
Tyr mr Vat Or HE BS ER
Serra Cn Pim Aro R=305 Nim
é Foo) x = (ur ta)t
9 *=I2861, p= nam
2
= = uam r-rtaps 4
WE More THAT RESUTS ARE INDEPENDENT OF
THE RAD Cl THE PISHS,
0.06
Spots 4d
Sit ks O06 3 St SD 06 dm,
19146 | From Frog 238 ox Pros. 19.40 THE
LEMETH OP fm EQUIVALE errors
FEmDIUM 18: ce É mn
te rÉ 4
a
Ea Bs R+ É.
F 8 e R
r + R
el. el. Bem 4%
2
g|- % EA ei” 27)
Al Fust p
4,2A,
For L=Api 22 x
e EE
- = 2.
RAR rR RE
eR(T-R) =ACe-R)
Since lP-B)IO, mE MAvE
or p= BY am
TRUE AGE EB! ANO BETCB, THA 65, MA arm 608
NeTims 17H87 Mg ha A
VE = 22 a
T=22, g er 3"
ro
E iimtomtarerrenesmeeecemrnseerees
AF
7 ramfz[e
Progirm RCA
AMP ITA = E,
tuhgeo
WE MAY CoMPUuE E RS Potts:
nas:
2=[3 (85h
1 + [o
BT ENE STE THE GUAMITY ABOVE IME 5 TRÉ CHANGE 14 E Anos DenoTEo 6% Duara <
(e
sie do
e [(ea
(st)
c- fra
143 (e 24 ne
22% Jets Ea ag /€ +
201
|
E
Tor
«|
E —————a
2” aj
ND The unnTy (2% 7 <) (s Devin Ex SREPAR = Red no <q
sena a c
PROBLEM 19.C1 low PROBLEM 19.C1 *
BASIC VERSIGN “cs FORTRAN VERSION *
a Comtestes
e
Definition of Synbols c Definition of Symbols
E
TH = amplitude of nacillations (degrees) c TH = amplitude of oscillations (degrees)
C = aintri/es e É + ainciva)
E = nua DY serios in bracket c D = sus of series àn breckot
Na number of teraa included 1n brackré E N = runber of turas includad in bracket
DELTA = change in À am nusber of feras is increased GC DELTA * change in B as nunber of teras is incressed
c
= amami) INTEGER TH
Xe PrrISo REALE, 1
PIO 0 aaa
PRINT memneseaoeenaomenaor Ke PI 7 1do.0
FOR TH = 39 TO 126 STEP do c
PRINT UBINS “ Aeplitude = 94% degraus! TH:PRINT WRITEto 1»
R=1 s2 FORMATO! — ="
DELTA = 1 PO 149 THe36 129,30
E = CEINtKATH/2») VRITE(a 26) TH
Petr e n Bracket MPRINT as FORMA fmplilude a "513, degrems"/)
1=1 Be 1.6
FORN=1 TO29 ter 1 DELTA = 1.8
FACTOR * (DAN 1)/(D4N5540 T = SINQGTH/2)
DELTA » DELTASFACTOR O 1= 1.6
B=B + DELTA wRITE e 36
TEN < 1 6070 sao 3» FORMAR N Brackat?,7)
PRINT USING * ” 8, DO 88 hes,28,1
FRINT USING“ 4.66224 “53 FACTOR = LUZ GN = 1.0)/(2.8M100
I=1+1- 1 DELTA = DELTA 4 FACTORes2
NEXT =P + DELTA
IF (NALT.T) GUTO BO
WRITE OD) N$B
“ FORMAT CT, 1247408 7.3)
Ta 1+1-d.608
e CONTIME
WRITE(2,397
180 CONTIMVE
END
SEE MEXT LREE PESR
Refear Berne of Prosas ue Cor MESAS
421
ema
E, sim ul
Úho7E: THE FORCE DUÉ To THE UNBRLANCE. 15
E mute (gro? <]
RO
b-feso)*
Ebogrem I2c3
LET:
AAA A
En flê
Ana Devo
2
AS Fome O
Denorzo BY Fa /N TRE ASA DERIVADO ANO
LV E mm Fortomne Plast)
a u
PROBLEM 19.03 tic PROBLEM 19.03 x
BASTO VERSION MES FORTRAN VERSION ,
0% | Cezaaa anta
£
Definition of Synbols £ Definition of Sytots
E
= weight of motor (1b) c d+ melght of motor (Ih)
K = spring constant Gb/tt) c K= spring constant (Lb/ft)
P.m circular fraquercy 0? fre vibration (rad/s) c P = circular fraquency of Tree vibration (rad/s)
c
WL = asgnitude of equivalent unbalance (1h) c Hi = sagnitude of equivalent unbalance (1h)
R = distance 6f HI froa adia of rotation (re) c R = distance of ML from axis of rotation (FE)
OMEGA = speei of anter (rpm) c OMESA = speed of motor — (rpe)
F = aaguitudo of centrifugel force dua to unbalance (16? | F = magnitude cf contrituçal forcu due to umbalance (ib)
XHAk = asptitude of vibration (Tt) £ XHO% » amplitude of vibration (ft) ,
xdaua secelerstion during vibration (16/32) e ANAL = canigua acreleration during vibration (f/am2)
E ç
Data REAL Ms Es Ko Ms Ro Po Jo Ma Po DENOM, EMOX, AMAL, E
LET M= 250 b INTESER OnEGa
LET 6= 32.2" tri/se c
LET Ke 758 Plh/in., for ore spring c Data
K = GMKHIE “express constant ef 4 springs in Ib/ft “= 258.6
Ba AETHI=S “oz 6. 32.2
me WI = Wi/l6 “express unsalance án pourda K = 188.6
as ET Re6 , «= sema
ro Ra Ri? Cuxprase Rin fest wi = 1.8
amo + “a a uiris.o
em PI mn GMAINID Ra 6
SOB J-BWPI/GS "factor to change rom into rad/s R=RAZ :
mer E
= M=W6 mama or motor PI = 4. BrATANCI.D)
330 P SOREKAM) E]
sao c
556 PRINT * OMEGA xHax Max new
B48 PRINT ron inches tee É = SORTCK/MI
376 PRINT c
E WRITE Ce) * OREDA XMAL amar
990 FOR OMEGA = 28 TO 1200 STEP 5a MRITERRO * rpm inches terem
seo F = CNI/GISRe(IAREGAI E RITERÇO ++
aa DENOS 1 = (HeMERA/P)-D c
2a XHAK o (F7K) /DENDA DO 106 OrEsa=I0a, 1208,50
“sao AMAM = XMANSCIAOMEBAI "E E = (WI/BHaReCTADMEGADASE
asa RM = RMARZIZ O “exprese AMA dn inches for grinting DENOM = 1 - LTNOMEGA/PIAAZ
«so PRINT USING = dee “OreSA, XHAR = 4F/6/DENM
pr PRINT USING * 48 444448 paer, AMA a ANAXA(TEDHEGA 492
«78 PRINT USING = aeb aus «ami XNAX = XNOReIE
sm NEXT WRITE (a 50) MEDA KMAIo AMA
se FORNATI2X, 14,12, F9. 6,7%, F9.0]
196 CONTINE
ESA so
rem mesa eax
so ros renina
ass ae «88%
Dee so «sBt6
e «1765
se “so «40
som 11764
sao ms ses. ves
a as -2. 1865
= asso =1.4887
786 eso —
ses 156 -1.t899
= ess -1.1B66
a eso. -1.2185
sa08 -PeggIHaS ss es
: eso ER somo Ciaçes
Er so LuEn brsisd ires
nse a gersao Eos ci
180 A. paIaso e ae
rea =1"781
224
000000 OCO TOCOCOCOCOCCOCOCOCCOOCCCOCCCLOCOCCC0 CCT
Br Det.
FE dura)" Ps [let io É
oe, REcALInA From Ey (12.53) Ea tmpe a
1
ZledecMora)
=(oya)ã
it fr fee E
xo fR o, Às :
GA DRE
425
|
i
!
646606546
h
e
e
o
e
0
“
»
e
º
10" msemmentaniinatasidavaraaro resi isa EsA RIAA EDU em | Dane
2a - PRDGLEM 19.04 + [er PROBLEN 49.04 º vo
3a a vó BASIC VERSION Io “o FORTRAN VERSION : : .
A e jo
E c
da + Definition of Bymbels € Détinition of Syabols
+ e :
e Wi = meight of motor tb) c W = melght of motor 1b) '
98 + & = spring constant (Ibgftt c K = spring constant (lb/rtt
196 + P = circular frequency of free vibration tradiad £ P =circular frequency of Tree vibration trad/s)
Esto L
os * W5 = sagnitude Of equivalent umbalanee (15) E ui = sagnitude Df equivalent unbalanco (by .
13 + R = distance of Wi froa axis of rotation (ft) c R = distance of VI fros axis of rotation (Tt
140» OHEBA = speed of motor” - tem z omEoa = spred of motor tres)
158 * € = atghitude of centrifugal force due to umbalance (lb! | E F = magnitude Of centrifugol forca dua to unbalanca (1h)
260 amar = amplitude DF vibration Crb) E amar = amplitude of vibration: (76
178 + arat » naxiaun acceleration during vibration (6/5252) E maximus accoleration during vibration tft/22)
189º PHI = phe difference (degrees) £ phasé difference (degrees!
158 * € = coefficient of viscous Somping b.sift) e confficiant Of viscous damping (Ih,6/1
eso + OC > critical Banping comtficient Clh.s/98) E critical danping comfficiamt (1h-g/ft)
ao - .
ae para REGLM, 6, Ko Who Ro Pio od Po DEN, MNA, AMA, Ps Cs CO
es uz Ha tb ANTESER OMEGA .
ms (E G-Bee feras E
25 VET K=988 rib/in.s for one spring E Data
ato Ka amkulz cexpresm constant of 4 eprings in 1h/ft W = 256.5
em rox 6. 22
209 “express unbalance in pourda Ke 8.8
290 emo K + epala
E >expresa Rin fest di = 1.8
Ha LETC-75 Plbes/ft ul = Wi/iá
ea R= 6.5
[308 PI = GemtNCIS Rene
2a de garita actor to change rpe into radiu came
E e
ass H=W6 “naus of sotor PE = 6 .BaATANI O)
26 P = RAMO o Raio
ae co= eus e
398 + na w/6
sos PRINT» OuEBA na aros Put P =» SORTIKAM
18 PRINTS rpa inches resta dágraos Ce = Emap
o mm . A
“50 + MIT ter
AMB FOR OMEGA » SUB TO 1200 STEP DO 19 FORMAT(! OMEGA max AMAR, 0
asa Fa (ML/G)AREÇIONESA) E + par
“es VEN = 4ê — (IN0NEGA/PI-D) uRITE tea)
ata PRE OTIBo CE EEN SC ISOMEDA/P)/DENGI 14 (PEV 190 2» FORMATO! rp inchom teresa”,
«Bs RNA CUP) /DENDMACOS A CPI /IBBAPHT) “see note bejom +... degrees!)
“se OMAk = AMHARIC TAEGA O man WRITE tes 2 +
sas KBAK = AMAXeIZ Pexpress MMA in inches for printino
E PRINT USING * susa “OMEGA, DO 100 neEsA=aUo, 1298,50
seg PRINT UBINS “MoMA rSxMar, E = qUi/oimReCTADHESNImE
53 PRINE USING “CMAS pax, DEN = 1 - (IMHEGA/PIME
sa PRINT USING = aa6.M6M" son PH a CATANCBU(C/0Ch*(TRIHESA/P)/DENON) 3 /4P1/1904
ssa er XAL > (4/6) /DENOH COSCAPI/LBAIPRIS :
RO = Exata CHRMEGAI (Ste mete tolo)
Kar = Mmareio
oneca VRITESO/SD) OMEGA, NMAx Max PMT
ne SO O FORNATCEK, LM S2R,E9.6 707.4, 7K4P7.3)
19 CONTINUE
sto em
me
e omega Max PuI
se rom inches
so E” omnes
pd xe “mares
ssa sas “oa1167
es «so :
E soa osso
E E -.sopsha
as usa - B8sa96
hd esa - gases
aa mo seria
1858 ss Tiogesos
e esa MoIHes
ee as “iseieo?
as “Loprego
1800 - opises
tese — BpL47A
. s198 —pólips -
use —serzos
156 = emasa
ore: THIS Pao *5 ceririo Flom do (1752) As Fottomes
Leal Re = Sd i