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peD artmentofM hce a cin alEngi reen ing

uS jb ce t oC d :e 5056EM / anyD m sci fo aM chines

Ye eS&ra mes :ret drIII - htV

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www.Vidyarthiplus.com

LECTURE NOTES

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DACS NE G ENI E EGELLOCGNIR

Departme tn fo Mechan ci la E gn ineering

buS emaN : anyD micsof nihcaM ery 5056EM:edoCbuS

aeY r C/ l sa s:III- lacinahceM A&B

TON SE OF EL S OS N

EJBO C :EVIT

dohtemehtdnatsrednuoT tsfo a cit f lanaecro y ddnasis y ciman f lanaecro y fosisM ce h na isms

oT s dut y th ue n barised l ee f fostcef nu b srotorniecnala an senigned .

atsrednuoT n td h oce n rotarbivfotpec y sy tdnasmets hei ar n la ysis

atsrednuoT n td h ogfoselpicnirpe v dnasronre gy .sepocsor

ER F NERE EC :S

Thom eBsa van T", h roe y fo asrehsilbuPSBC,"senihcaM n rtsiDd ib 891,srotu 4.

Gh hso A a. n llaMd i kc A roehT",.K. y fo ceM h asmsina n liffA,"senihcaMd i tsaEdeta -

W tse Pres Ps v .t L dt . eDweN, lhi .8891,

hS i elg y J .E. an Ud i rekc T",.J.J h roe y fo asenihcaM n warGcM,"smsinahceMd -Hill I, n ,.c

991 5.

oaR J.S k kuDdna. i itap ",.V.R M amsinahce n hcaMd i roehTen y yeliW," - nretsaE

miL i hleDweN,det i 1991, .

oJ h naHn n aha n petSd h ",.C.Rsne M ce h foscina hcaM i iV,"sen va l wo - rP i edutSdec nt

dE iti 9991,no .

daS h Su in hg Th yroe hcaMfo i sen tacudEnosraeP i 2002,no .

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DNI EX

TINU I- ecroF An la y sis

)1( tnI r udo c noit

)2( notweN sLaw

)3( sepyT fo of r ec anA lys si

)4( Pr picni le fo epuS rPos noiti

)5( Fr ee ydoB gaiD r ma

)6( AD l me eb r st Pr elpicni

)7( Dy an m ci anA lys si fo F uo r ab rMec msinah

)8( uT r gnin oM me tn gaiD r ma

)9( S gni le yc l edni r buod leac gnit enigne

)01( uT r gnin mo em tn gaid r ma for4- ts r ko e C.I e enign

)11( uT r gnin mome tn gaid r ma foramul it yc l redni enigne

)21( Fluc noitaut fo Ener yg

)31( Fl itautcu on fo pS ee d

)41( aM xim mu fluc noitaut fo ener yg

)51( oC ffe ici e tn fo fluc itaut on fo e en r yg

)61( oC e ff ici e tn fo fluc itaut on fo s deep

)71( enE r yg ots red ni fl leehwy

)81( Fl hwy ee l ni nup c gnih pre ss

)91( maC scimanyd

)02( Ex lpma ePr bo l sme

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NU IT I - For ec A an lys si

tnI)1( r udo c :noit

fI eht arelecca t noi fo mo gniv sknil ni a msinahcem si gninnur with co elbaredisn ma o tnufo raenil ro/dna ralugna arelecca t ,snoi reni t ai fo secr era detareneg dna eseht reni t ai secrof osla

tsum eb crevo o em yb t eh dr gnivi m oto r sa na idda tion ot t eh fo secr rexe ted yb t eh ext anre l lo daro w kro the m msinahce .seod

)2( notweN s La :w

Fi sr t waL

evE r oby dy lliw p tsisre ni its state of tser or of u ofin rm om t noi c( o sn t tna ve ol cit )y ni athgiarts enil sselnu ti csi o otdellepm tahtegnahc stat ybe fo secr desserpmi on it. sihT aem ns t tah

ni t eh ecnesba o af non - orez ten fo ,ecr t eh nec t re fo ssam o af ob d iey t reh si ta r tse or mo sev at a

colevtnatsnoc ity.

dnoceS waL

A ob dy of sam s m su tcejb ot a fo ecr F u gredn o se an a cc e arel tion a t tah has t eh s ema

cerid t noi sa t eh fo ecr dna a gam nit edu t tah si cerid t yl rp oport lanoi to t eh fo ecr dna esrevni lyroporp t lanoi to t eh ,ssam ,.e.i F= ma. lA ter an t ,ylevi t eh tot la fo ecr pa p deil on a body si lauqe to

raenilfoevitaviredemiteht momen mut fo eht b do y.

ihT r aLd w

ehT um t lau secrof of ca tion a dn caer t noi eb t neew t ow seidob era ,lauqe o pp o is te dnacolli en ar. sihT snaem t tah revenehw a tsrif ob dy rexe ts a fo ecr F no a ces o dn ob d ,y t eh ces o dn

ob dy rexe ts a fo ecr -F on t eh tsrif bod .y F a dn -F era lauqe ni gam nit edu dna o pp o is te nidi tcer i .no sihT wal si so em t derrefersemi to sa t eh ac noit -reac noit al w, with F dellac t eh " ca t "noiand -F tcaer"eht ion"

offosepyT)3( r anAec lys :si

muirbiliuqE fo m wsrebme i tht wo f secro

muirbiliuqE fo m wsrebme i eerhtht f secro

muirbiliuqE fo m wsrebme i tht wo f euqrotdnasecro

muirbiliuqE fo m wsrebme i tht wo c puo l se .

muirbiliuqE fo m wsrebme i ht f ruo f .secro

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P)4( r picni el epuSfo r Pos :noiti

emoS t semi t eh rebmun of xe t lanre fo secr dna reni t lai fo secr ca t gni on a msinahcem are

oot hcum for lacihparg so ul t .noi nI t sih esac ew pa p yl t eh em t doh of prepus o is t .noi sU ingnoitisoprepus eht e eritn metsys si rb o nek pu ni to )n( rp o ,smelb erehw n si t eh nu r ebm of fo ,secr

yb gniredisnoc eht lanretxe dna reni t lai fo secr of hcae knil idni v yllaudi . esnopseR of a r aenil

s sy t me to lareves fo secr ca t gni mis ult ena o ylsu si lauqe to t eh mus of pser o sesn of t eh s sy tem tothe f isecro n vid i llaud y. esuaceblufesusihcaorppasihT i repebnact f ro m bde y llacihparg y.

F)5( r ee gaiDydoB ram:

A eerf ob dy d rgai am si a p ci t lairo r rpe e nes tation oft ne u des yb phys sici ts dna e sreenign

ot ezylana t eh secrof act gni on a ob dy of ni t sere t. A eerf ob dy d rgai am sho sw a ll fo cr es of a llt sepy gnitca on t sih ob d .y gniwarD hcus a d r gai am nac dia ni so gnivl for t eh nknu o nw fo secr or

eht auqe t snoi of om t noi of t eh bod .y aerC t gni a eerf body d r gai am can ekam ti reisae tosrednu t dna t eh fo ,secr dna t seuqro or nemom t ,s ni aler t noi to o en na to reh dna tseggus t eh rp o rep

stpecnoc ot ylppa ni o redr ot dnif t eh ulos t noi to a r p o .melb T eh d rgai a sm era a osl desu sa a

lautpecnoc ecived ot pleh nedi t yfi t eh ni t lanre fo secr rof ,elpmaxe raehs secrof dna gnidnebmomen nist b smae evederahcihw l wdepo i urtsniht c serut .

)6( AD el ebm r st Pr picni el :

s'trebmelA'D pr ,elpicni osla nk o nw sa t eh gaL r gna e A'd lem eb rt pr picni el , si a

tnemetats o ehtf lacissalclatnemadnuf swal of itom o .n tI si retfademan csidsti o ,rerev t eh nerF chtsicisyhp dna amehtam t naici naeJ el dnoR d rebmelA' t. ehT pr elpicni stat se t tah t eh sum of t eh

secnereffid eb t ehtneew casecrof t nogni a s sy t me dna t eh t edemi r avi t vi es of t eh mo nem ta of t eh

sy mets i aflest l nagno y lautriv di snoctnemecalps i wtnets i tht h iartsnoce n fost seht y .orezsimets

D)7( y iman c anA lys fosi F uo r ab r M ce :msinah

A uof r- ab r l gakni e or pmis ly a 4- ab r or uof r- ab r si t eh tselpmis mo elbav nil k .ega tIsisnoc ts of r uof r digi ob d sei dellac( srab or ,)sknil hcae a tt dehca ot t ow ot sreh yb elgnis jo ni ts or

p ovi ts ot fo mr lc o es d ol o .p ruoF - srab era elpmis inahcem s sm co mm on ni cinahcem alangisedenihcamgnireenigne nd f lla un dutsehtred y fo ki tamen i sc .

Dyn Acima n la y tacorpiceRfosis in gneg i sen .

trenI ia f aecro n lanaeuqrotd y bsis y n giewgnitcelge h fot noc n orgnitce d.

eV l co i yt tareleccadna i fono otsip n.

evralugnA l co ity tareleccaralugnAdna i fono itcennoc n dorg .

lanAeuqroTdnaecroF y sis i cern i tacorp in enigneg n ge l itce ng eweht i fothg noc n tce i gn

or d.

DtnelaviuqE y laciman Sy mets

tanimreteD i fono two m fosessa iuqe v ela n dt yn lacima sy mets

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5056EM:edoCbuS uT)8( r oMgnin me gaiDtn r :ma

gninrutehtfonoitatneserperlacihpargsimargaidtnemomgninrutehT tnemom knarcro

fe f tro f ro v ra i sopsuo iti f osno arc n .k

)9( S gni le yc l edni r buod l ae c :enignegnit

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uT)01( r gnin mo em gaidtn r ma for 4- ts rok C.Ie e nign e:

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uT)11( r momgnin e gaidtn r ma for a mul ycit l redni e enign :

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buS` EM:edoC 5056

)21( Fluc itaut o enEfon r :yg

tniecnereffidehT h ike n te i grenec i iopehttase n lacsit l tde he m mumixa f tautcul i fono

en gre y.

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)31( Fluc itaut o pSfon e de :

dnamumixamehtneewtebecnereffidehtfooitarehtsadenifedsisihT ralugnamuminimcagnirudsdeeps y ehtotelc m torfodeepsnae ati f ono th arce n ahsk f .t

)41( aM xim mu fluc fonoitaut e en r :yg

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buS` EM:edoC 5056

oC)51( ffe ici e fotn fluc itaut o fon e en r :yg

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oC)61( e ff ici e fotn fluc itaut o fon s :deep

enE)71( r otsyg re nid fl ehwy el:

A fl leehwy si a or tat gni ssam t tah si desu sa na e ren gy eser r riov ni a am c .enih tI sbrosba

rene gy ni t eh form of k eni t ci rene g ,y ud r gni tho es ep rio sd of r c a kn rotation w neh ca tual t gninrumo tnem ehtnahtretaergsi siser t gni mo tnem dna r reneesaele g ,y wyb ay o rapf t gni iw th so em of

i st K lautcaehtnehw,E. gninrut m sitnemo l tsse h itsiserehtna ng m tnemo .

)81( Fl hwy ee l nupni c pgnih re :ss

lfehT y desusleehw f emirpro m caetutitsnocsrevo l borpfossa l gnitsiserehthcihwnisme

euqrot si ssa u dem ot eb co sn t tna dna t eh ivird ng euqrot av r .sei sleehwylf desu ni ,gnihcnup

r evi t gni dna ralimis senihcam co sn titute ona t reh ssalc of r p o smelb ni hcihw t eh ca tua (l dr )gnivigninrut mo tnem dedivorp yb na cirtcele om t ro si erom or ssel tnatsnoc tub t eh siser t gniuqrot e(l )dao v ra i se .

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:edoCbuS 5056EM

)91( maC :scimanyd

msinahceM sedivorp a non - raenil O/I aler tio pihsn . tnereffiD msinahcem ekil elgnis or

lum ti- eerged of deerf o ,m tnettimretni om t noi inahcem s sm dna segaknil etc. evah tnereffid O/ItaleR i .pihsno nehW ew nac ton bo t nia a rec t nia fu cn t snoi rf om t eh llew nk o nw em c ,smsinah ew

us macae m ce h na ism. tI i foeergedenoas f owtfomsinahcemmodeer m csienO.sknilgnivo am

an td h toe h sire f lo l rewo .

Ri adig n tsaled ic b ydo smac y ets m.

An la y fosis ecce n rt i macc

Pr bo lem nos C ma f lo l srewo y ets m.

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E)02( x lpma e Pr bo l :sme

)1 ehT airav t noi of narc k hs a tf t euqro of a fo r u c rednily ep trol e enign may be

rppa o amix t yle er p neser t de yb t gnika t eh to euqr sa orez for k narc ang sel 0 dna 81 0 dna as 062

mN for knarc selgna 20 dna 45 , t eh ni t aidemre te portio sn of t eh to euqr arg ph gnieb stra thgi

lines. T eh c elcy si gnieb detaeper ni eve ry f lah ver o ul tio .n ehT a egarev sp dee si 006 rpm.gnisoppuS t tah t eh enigne dr sevi a am c enih gniriuqer co sn t tna to ,euqr ed t enimre t eh ssam of t eh

fl leehwy of ar d sui of g ary t noi 052 ,mm hcihw tsum eb rp o dediv os t tah t eh ot t la av r ai tion of

llahsdeeps b oe n .tnecrepe

)2 A s elgni c rednily rev t laci e enign sah a bo er of 003 mm a dn a stro ek of 004 .mm ehT

cennoc t gni rod si 1 m lo gn a dn t eh ssam of t eh r rpice o ac t gni rap ts si 041 .gk on t eh expansion

stro ,ek iw th t eh knarc ta 03 rf om t eh top daed nec t re , t eh gas p sser u er si 7.0 aPM . If t eh e enign

tasnur 052 enimreted,mpr ( )i ten caecrof t )ii(notsipehtnogni ser ult tna daol on t egdugeh on p ni

( )iii t tsurh on t eh c rednily wa ,sll a dn ( )vi t eh speed abo ev w ,hcih ot r eh t sgnih r iame n gni t eh

nipnoegdugeht,emas l uowdao l erebd v dnidesre i tcer ion.

)3 A rev t laci do elbu ca t gni st mae e enign sah a cyl r edni 003 mm d emai t re dna 054 mm

tasnurdnaekorts r002 p .m T rpicereh o ac t rapgni t asahs ssam o 522f gk a dn t eh p si ot rn o sid 05

mm d emai t .re ehT cennoc t gni dor si 2.1 m lo .gn nehW t eh knarc sah t denru t rh o hgu 521 rf om

t eh top daed nec t re t eh st r pmae e eruss evoba t eh p si ot n si 03 Nk m/2

a dn below t eh p si ton si 1.5

kN/m2. aC l uc l eta

(i arC) nk- f enip f atro nd

(ii gninrutevitceffeehT) momen arcehtnot n ahsk ft .

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DNI EX

U IN T II B LA ANCI GN

)1( I tn r itcudo on

)2( aB l na c gni fo r gnitato sam ses

)3( S itat c ab l gnicna

)4( cimanyD gnicnalab

)5( Var suoi ac ses fo ab l gnicna fo r gnitato m sessa

)6( aB l na c gni fo a gnis ler gnitato m ssa yb gnis lemassr gnitato ni ht e as mepl ena

)7( aB l na c gni fo a gnis ler gnitato m ssa yb owt mas ses r gnitato ni t eh id f tneref pl ena

)8( aB l na c gni fo a ves er la m ssa esr gnitato ni samepl ena

)9( aB l gnicna fo s ve er la m sa s se r gnitato id ff tnere pl ena

)01( aB l na c gni fo Rec pi roc gnita m sa s se

)11( Primary dna adnoces ry abnu l decna for sec fo picer roc gnita ap r st

)21( aB l na c gni fo s gni le yc l edni re enign

)31( Ba gnicnal fo laitreni f secro ni eht m itlu - ilyc nd re en enig

)41( Par lait ab l gnicna fo oL com vito es

)51( aV r noitai fo Tr evitca of r ec

)61( yawS i gn puoC le

)71( H ma m re bl wo

)81( aB l na c gni fo Inl ni ee senign

)91( aB l na c gni fo r laida e nign es

)02( Exam lp ePr bo le sm

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NU IT II BAL CNA ING


gnicnalaB si t eh rp o ssec of animile t gni or ta tsael r gnicude t eh rg o dnu fo secr a /dn or

m .stnemo tI si deveihca yb c gnignah t eh acol tion of t eh ssam cent ser of .sknil gnicnalaB ofor t gnita strap si a llew kno nw rp o .melb A or tat gni ob dy iw th dexif r to at noi ax si nac eb fully

decnalab e.i . lla t eh reni t ai secrof dna mo nem t .s For msinahcem gniniatnoc sknil or tat gni abo tu

sixa hcihw era ton ,dexif ecrof gnicnalab si ,elbissop mo tnem gnicnalab yb it fles may eb,elbissop tub htob ton po .elbiss eW yllareneg try to od of r ec .gnicnalab A ylluf ecrof ecnalab si

bissop l ,e b natu y tca i nino f ecro b esgnicnala v ehtere m emo n abt lan gnic .

aB)2( l fognicna r gnitato ma ss es:

ehT rp o ssec of r p o gnidiv t eh ces o dn ssam ni o redr ot nuoc t tcare t eh e tceff of t ehec n irt f lagu f foecro the fi tsr m acsissa l abdel l icna n torfog a it n sessamg .

)3( S itat c ab l na c :gni

ehT ten d cimany fo ecr ca t gni no t eh tfahs si lauqe to .orez sihT qer u ri es t tah t eh enil of

ca t noi of t eerh nec tr lagufi fo cr es mu ts eb t eh sa em . nI ot r eh wo ,sdr t eh nec t er of t eh sessam of

seht y tatorehtfosixaehtnoeiltsummets i .no hT i tsis h oce nditi no f ro sta cnalabcit i .gn

)4( cimanyD :gnicnalab

ehT ten co elpu eud ot cimanyd secrof ca t gni on eht hs a tf si lauqe to orez . ehT ciarbeglamus ehtfo m ynatuobastnemo tnitniop h pe l .orezebtsumena

V)5( ar acsuoi s abfose l na c fogni r :sessamgnitato

fognicnalaB tatorelgnisa in bssamg y si elgn m torssa ati gn i tn h emase

plane.

cnalaB i fogn tatorelgnisa in bssamg y owt m torsessa ating in th f ide f ere nt

plane.

aB lanci f ogn esa v lare m torsessa a it n pelgnisnig lane.

cnalaB i fogn larevesa m torsessa a it n nig fid f ere n pt l .sena

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aB)6( l afognicna gnis le r gnitato m gnisybssa l ame ss r htnignitato e as m pe l :ena

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aB)7( l gnisafognicna le r gnitato m owtybssa mas ses r nignitato the id ff ptnere l na e:

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aB)8( l safognicna e ev r la m sa s se r snignitato a em pl na e:

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aB)9( l fognicna s ve er la m sa s se r fidgnitato f ptnere l na e:

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aB)01( l Rfognicna e pic roc gnita mas :ses

ocnegnicnalabssaM m wasessap i arraed y fo m eserusae mploy ootde b trapniat i la ro

oc m ocetelp m tasnep i no f treniehtro i la f dnasecro m ifostnemo n eaitre m itana ng f mor the

arc n ahsk f essat m lb y. llanretxeerasessamllA y alab n wdec h ne no f trenieer i la f rosecro momen st

ifo n tre i msnarteraa i tdett h hguor beht l ehtotkco stuo i .ed ereht,revewoH m lanretnigninia f secro

and m busstnemo j eehttce n enig m uo n bdnast l ravotkco i suo l edsallewsasdao f ro mi aseit nd

vi rotarb y stre ss es cisabehT. l sagybdesopmisdao - adesab n trenid i la f secro

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P)11( r ami r adnocesdnay r abnuy l picerfosecrofdecna roc apgnita r :st

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aB)21( l fognicna s gni le yc l edni r e :enign

A elgnis c rednily enigne rp o secud t eerh niam v arbi t snoi . nI gnibircsed them ew w lli

emussa taht eht c rednily si rev t .laci sriF t ,yl ni na enigne iw th on gnicnalab hgiewretnuoc t ,s t erehwo dlu eb na ne o suomr arbiv tion r p o decud by t eh nahc ge ni mo nem tum of t eh p si to ,n g du eg on

,nip cennoc t gni dor dna tfahsknarc o ecn eve ry revo ul t .noi aeN r yl lla lgnis e-c r ednily rc a hskn aftsetaroprocni gnicnalab hgiew ts ot ecuder t .sih elihW t eseh hgiew ts can lab a ecn t eh crank hs a tf

,yletelpmoc t yeh tonnac yletelpmoc ecnalab t eh om tion of t eh p si ot ,n for t ow .snosaer ehT tsrif

nosaer si t tah eht gnicnalab hgiew ts evah ho zir ont la om tion sa we ll sa rev t ci al motio ,n osgnicnalab t eh ylerup rev t laci m to noi of t eh p si ot n yb a narc k hs a tf thgiew sdda a ho zir ontal

vi tarb ion. T eh ces o dn er ason si t ah t, edisnoc r gni won t eh rev t laci m to noi o ,yln t eh rellams p si ot ndne of t eh cennoc t gni rod il( tt el )dne si lc o res ot t eh regral tfahsknarc dne gib( )dne of t eh

cennoc t gni dor ni dim -stro ek t nah ti si ta t eh top r o ttob om of t eh stro ,ek aceb u es of t eh

gnitcennoc .elgnas'dor oS gnirud t eh 081 or tation rf om im d-stro ek t hguorh top- daed - nec t re dna

kcab ot dim -st ekor t eh ronim ubirtnoc t noi to t eh sip t s'no d/pu o nw tnemevom rf om t ehcennoc t gni ro s'd egnahc of elgna sah t eh emas cerid t noi sa t eh rojam cont ubir tion to t eh p si ot s'n

nwod/pu tnemevom rf om t eh d/pu o nw tnemevom of t eh rc a kn p ni . By noc t sar t, gnirud t eh 81 0or t ita on r f om dim -stro ek t rh o hgu ttob om- daed - nec t re dna kcab ot dim -stro ek t eh nim or

noitubirtnoc t d/pus'notsipehto o tnemevomnw rf om t cennoceh t gni egnahcs'dor o sahelgnaf t ehisoppo te cerid t noi o ehtf rojam ubirtnoc t otnoi sipeht ot s'n d/pu o mnw ove tnem rf om t eh d/pu o nw

mo tnemev ehtfo knarc p .ni ehT p si ot n t f ereh o er slevart saf t re ni t eh top f lah of t eh c rednily t nah

ti seod ni t eh mottob ,flah elihw t eh om tion of t eh narc k tfahs hgiew ts si s suni o .ladi ehT rev t ci alom t noi of t eh p si ton si t ofereh re ton iuq te t eh s ema sa t tah of t eh lab anc gni hgiew t, os they ca t'n

lecnacotedameb pmoctuo l lete y.

noceS d ,yl t ereh si a arbiv tion r p o decud yb t eh egnahc ni deeps dna t reh efo er k eni t cirene gy of t eh p si to .n ehT tfahsknarc lliw dnet ot ls ow do nw sa t eh p si t no sdeeps pu dna sba o sbr

rene g ,y a dn to deeps pu niaga sa t eh p si ton sevig pu e ren gy in slowing do nw ta t eh top dnattob om of t eh stro .ek sihT arbiv t noi sah t eciw t eh neuqerf cy of t eh tsrif arbiv t ,noi dna gnibrosbai osit ne f tcnu i fono th lfe y eehw l.

,yldrihT ereht asi biv rat r pnoi o decud yb t eh tcaf taht t eh enigne si onl py ro gnicud po rewtgnirud h .ekortsrewope anI uof r-st sihtenigneekor arbiv t ehtflahevahlliwnoi neuqerf c foy t eh

tsrif arbiv t ,noi sa eht c rednily serif ecno eve ry t ow ver o ul tio .sn In a two-stro ek ,enigne ti willh teva h emase f cneuqer y tsa h rife s vt i tarb i ivsihT.no b tar i bdebrosbaoslasino y lfeht ywh lee .

aB)31( l enifognicna r lait for htnisec e mul it - yc l dni er e nign e:

nI lum ti-c r ednily senigne eht um t lau co nu t care tio sn of t eh irav o su co pm onents ni t ehknarC tfahs bmessa ly era o en of t eh nesse t lai tcaf o sr ed t imre ning t eh s cele tion of t eh knarC

arugifnocstfahs t htiwdnanoi ti ngisedeht of t eh enigne it .fles ehT reni t oflai r sec era decnalaB ifeht mmoc on nec t er fo ivarg ty for lla mo gniv hsknarc aft- messa b yl co pm o nen ts seil ta t eh

s'tfahsknarc ,tniopdim e.i . fi eht rc a tfahskn si emmys t lacir sa( deweiv rf om t eh rf ont). Thes'tfahsknarc s emmy try level nac eb denifed gnisu eg o em t lacir neserper tat snoi of s1 t- dna dn2 -

redro secrof rats( .)smargaid ehT dn2 o redr rats margaid rof t eh four- r ednilyc ni - enil eng eni sitemmysa r ,laci gninaem taht siht o redr si carahc t dezire yb natsbus t lai eerf reni t lai Fo .secr Th ese

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secrof nac eb decnalab gnisu t ow co nu t fahsre ts rotat gni ni o isopp te cerid tio sn ta elbuod t eh ar tefo arceht n ahsk f cnaL(t h sretse y ets m .)

)41( Par ablait l na c fogni Loc vitomo es:

aV)51( r Tfonoitai r ofevitca rce:

ehT ser ult tna decnalabnu fo eudecr to t eh c ,srednily alo gn t eh enil of stro ,ek si kno nw asart c evit f .ecro

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buS 5056EM:edoC

yawS)61( i puoCgn l :e

ehT coup el sah swa gniy e tceff ba o tu a rev t ci al ax ,si dna t sdne to ws ay t eh eng eni

yletanretla ni kcolc esiw dna na t esiwkcolci d ceri tio .sn ecneH t eh co elpu si kno nw sa ws a gniy

puoc le.

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H)71( amm re bl :wo

ehT mixam um ingam t edu of t eh u decnalabn fo ecr la o gn t eh prep end ci u ral to t eh enil of

ts r eko i ks n nwo aHsa mm bre l .wo

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aB)81( l fognicna Inl ni e e enign s:

inA n- wenosienigneenil h tllaniere h ce y o,enilelgnisanidegnarraerasrednil ne b dnihe

eht ot r eh sa amehcs t yllaci acidni t de ni giF . Ma yn of t eh regnessap srac fo dnu on I naidn ro sdahcus sa uraM ti ,008 ,neZ naS t ,or adnoH iC t ,y Ho adn RC - ,V dna To oy ta r oC o all a ll evah ruof

rednilyc ni - enil .senigne hT us t sih si a co mm o yln lpme o dey enigne dna ti si of ni t tsere ot su otun atsred n td h lanae y fosis i tsst a foet b ecnala .

For t eh ekas of icilpmis ty of ylana s ,si ew ssa u em t tah lla t eh c srednily era nedi t laci ,.ziv ,r ,

and are as me. torehttahtemussaewrehtruF a sessamgnit h odecnalabneebeva ut f llarocy asrednil n eraewd lef wt i lnoht y the f toteudsecro h cere i itacorp ng m sessa .

aB)91( l fognicna r laida e nign es:

A ar d enignelai si o en ni hcihw lla t eh c srednily a er degnarra cric u refm ent yllai sa hs own

ni esehT.giF senigne erew iuq te ylralupop us de ni farcria ts ud r gni dlroW raW .II Su esb euq ntehtotdelsenibrutsag/maetsnistnempoleved raen xe t cni t noi o .senigneesehtf tirevewoH ssi t lli

seretni t yltrohsssucsidllahsewstlusertnageleemosfoweivniecnalabfoetatsriehtydutsotgni .ruO em t doh of ylana s si sniamer nedi t laci to eht suoiverp esac i. ,.e ew rp o deec with t eh

pmussa t tahtnoi erasrednilyclla dnalacitnedi t eh c erasrednily decaps ta finu or nim ter lavuora nd ceht i ucr mf ecnere .

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E)02( x lpma e Pr bo l :sme

)1 tfahsA seirrac ruof gnitator sessam ,A dnaC,B yletelpmocerahcihwD .decnalab The

,Bsessam C a dn D era 05 ,gk 08 gk a dn 07 gk cepser t evi l .y T eh sessam dnaC D am ke ang sel of

09 dna 91 5 cepser t ylevi with ssam B ni t eh emas .esnes ehT sessam ,A ,B C dna D era

tadetartnecnoc 57suidar ,mm 001 ,mm 05 mm dna 08 rmm e ceps t .ylevi T eh p enal of or tation ofsessam B dna C era 052 mm rapa t. enimreteD ( )i t eh edutingam of ssam A dna its a r alugn

sop iti (dnano ii sopeht) iti pno l aAsena n .Dd

)2 sknarcehT o af t ow ,rednilyc delpuocnu edisni c rednily locomot evi era ta ir g th a selgn

dna era 523 mm lo gn . ehT c srednily era 576 mm .trapa ehT or tat gni ssam rep c srednily era 200

gk ta knarc p ni dna t eh ssam of t eh icer pro ac t gni rap ts rep c rednily si 042 .gk T eh w leeh nec t re

senil era 5.1 rapam t. ehT elohw of t eh or tat gni dna t ow t sdrih of t eh rpicer o ac t gni sessam era ot

eb decnalab dna t eh lab a ecn sessam era to eb pla dec ni t eh p nal es of t eh r to ation of t eh dr gnivi

sleehw ta a suidar o 008f .mm dniF ( )i t eh ingam t edu dna id r ce tion of t eh gnicnalab .sessam (ii)

edutingameht o elpuocgniyawsmumixam)vi(dnaecrofevitcartninoitairav)iii(wolbremmahf

arcata n fodeepsk pr042 m.

)3 )i( ruoF sessam m1, m2, m3 dna m4 dehcatta ot a gnitator tfahs no t eh emas p enal era

002 ,gk 003 ,gk 042 gk dna 062 gk cepser t evi ly. ehT co pserr ond gni iidar of or tat noi era 2.0 ,m

51.0 ,m 52.0 m dna 3.0 m re ceps t ylevi a dn t eh a selgn eb t neew evisseccus masses a er 45 , 75

.531dna dniF isopeht t noi dna ingam t edu of t eh ecnalab am ss iuqer r ,de fi t eh idar us of or tation

i 2.0s m .

( )ii nialpxE iw th taen eks t ,sehc gnicnalab of elgnis ver o gnivl ,ssam yb sessam ni t ow

fid f ere n alpt n toranise a it n sg y mets

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DNI EX

UNITI II FR EE IV BRATI SNO

)1( I tn r noitcudo

)2( isaB celeme stn fo biv r ita on ys stem

)3( Ca su es fo biv r ita on

)4( Eff stce fo biv r ita on

)5( Me ht o sd fo re noitcud fo biv r noita

)6( sepyT fo biv r ota rym noito

)7( Ter sm su ed biv r ota rym ito on

)8( Degr see fo fr modee

)9( S gni le ged ree fo fre mode sys met

)01( owT ged ree fo fr modee system

)11( sepyT fo biV r ota rym ito on

)21( sepyT fo noitarbiV

)31( gnoL i lanidut biV r noita

)41( Free adnu m dep l lanidutigno biv r snoita

)51( aN tur la fre uq e ycn fo fr ee adnu mpedl lanidutigno biv r noita

)61( aviuqE l ne t its ff ness fo spr gni

)71( gnipmaD

)81( sepyT fo gnipmad

)91( gnipmaD tneiciffeoC

)02( tnelaviuqE gnipmad tneiciffeoc

)12( depmaD noitarbiV

)22( gnipmaD rotcaf

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)32( agoL r hti micdecr me e tn

)42( Tr evsna rse biV r noita

)52( ihW rl gni fo s ah ft

)62( oT rs lanoi biV r noita

)72( oT rs lanoi biv r noita fo a gnis ler oto rs metsy

)82( oT rs lanoi biv r noita fo a owt r roto s tsy em

)92( oT rs lanoi ly aviuqe l tne ahs ft


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UNIT I II FR EE IV BRATI SNO


nehW a s sy t me si cejbus t de ot na ini t lai sid t ecnabru dna t neh tfel eerf ot arbiv te on its,nwo eht luser t gni arbiv t snoi era re derref ot sa fr ee arbiv t snoi .Fr ee biv r noita srucco nehw a

lacinahcem s sy t tessime iwffo t nah ini t lai tupni dna t dewollaneh ot arbiv te r f e yle . E max p sel ofsiht t epy of arbiv t noi era pu gnill a dlihc kcab no a gniws dna t neh el tt gni og or ih tt gni a t gninu

krof dna gnittel ti .gnir ehT lacinahcem s sy t me lliw t neh arbiv te ta eno ro mo er of its an" tur la

f a"seicneuqer n ezotnwodpmadd ro.

isaB)2( c ele em bivfostn r ita on sys :met

M Irossa n tre ia

rpS ingi eRrossen s rot ing element

Di emeleevitapiss n o(t f lacnet l adde m )repcxelanretxE i tat i no

C)3( a bivfosesu r :noita

abnU l na ec : sihT si yllacisab ni ecnerefer to t eh or tat gni b do .sei ehT u neven d si tr ubi tionof ssam ni a rotat gni body contr ubi t se to t eh bnu a ecnal . A og od elpmaxe of u ecnalabn re al t de

arbiv t noi wo dlu eb t eh arbiv t gni trela ni o ru mo elib pho .sen ereH a llams ma uo tn ofdecnalabnu iew g th si rotat de ayb mot ro gnisuac t eh rbiv ation w hcih am k se t eh mo elib pho en to

vi etarb . You dluow evah epxe r decnei eht emas tros fo arbiv t noi gnirrucco ni ruoy rf o tn lo deda

gnihsaw m hca i tsen h etta n ivotd b ehtgnirudetar spi nn ing .edom

asiM lignme :tn sihT si a on t reh rojam esuac of iv b ar t pnoi art niylraluci senihcam t tah era

bnevird y m sroto naro y to h irpre me mov .sre

tneB :tfahS A or tat gni tfahs taht si tneb osla secudorp eht eht arbiv t gni tceffe ecnis til tatortisesso i libapacno i tuobayt i retnecst .

sraeG ni eht ihcam ne: ehT ge sra ni t eh enihcam always t dne to pro ecud arbiv t ,noi

ylniam eud to t r ieh .gnihsem hguohT t sih may eb contro dell to emos ext ne t, yna pro melb ni t ehraeg b etxo n otsd ge net h wdecna i .esaeht

aeB r :sgni tsaL tub not t eh sael t, ereh si a rojam cont ubir tor for arbiv tio .n nI ojam rity ofsesaceht e ev r iniy t rplai o smelb t ra t nis t eh agaporpdnasgniraeb t otse t tsereh of t eh srebmem of

eht .enihcam A gniraeb ved o di of acirbul t noi t sdne ot raew tuo tsaf dna sliaf qu ,ylkci tub feb o ersiht si on t deci ti segamad t eh iamer n gni co pm o nen ts ni t eh am c enih dna na init lai l oo k wo dlumees sa fi so gnihtem dah enog gnorw iw th t eh rehto co nenopm ts gnidael ot t eh aeb r gni .eruliaf

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E)4( ff bivfostce r ita o :n

B)a( ad stceffE :T eh rp e ecnes of arbiv tion ni yna lacinahcem sys t me rp o secud u nawn t de no ,esi hgih

,sesserts op or ilibailer t ,y raew dna amerp t eru eruliaf of r ap t .s arbiV t snoi era a taerg so ecru ofh mocsidnamu f ehtnitro f mro fo hp y dnalacis m latne iarts n .s

)b( GoodE :stceff

A arbiv t noi seod lufesu wo k r ni lacisum nemurtsni t ,s arbiv t gni ,sneercs s ,srekah iler vehpniniap ysi to h pare y.

hteM)5( o fosd re ud c bivfonoit r noita :

- nu balan siec i st m abos,esuacnia lan f ognic rassecensistrap y.

- isu ng sh akco b ros b re s.

- isu n dg y tarbivciman i no rosba b .sre

-pr vo i eercsehtgnid n fi(s n otsiesio b )decudere

)6( Ty bivfosep r ota ry m noito :

F Veer ib tar i no

VdecroF ib tar i no

T)7( erms su e bivd r ota ry m :noito

miT)a( e ep riod o( r ep) r doi fo biv r :noita

tI si t eh t emi t neka yb a arbiv t gni ob dy to taeper t eh motion itself.t emi irep od si su ually

ex serp s de i esn conds.

)b( yC cle:tI i ts he m to i ocno m onidetelp n ite m repe i do .

c( )Per idoi c noitom :A m to i staeperhcihwno i aflest f lauqeret in lavret fo t mi .e

pmA)d( l eduti X( )

T eh mumixam tnemecalpsid fo a arbiv t gni ob dy rf om t eh naem po is t noi . ti si lausu lyex serp s limnide limet r e .

e( )Fre uq ency )f( ehT num f oreb cy ocselc m nidetelp on dnocese i dellacs f ycneuqer

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geD)8( r ffosee r modee :

ehT im n mumi nu r ebm of nepedni d tne oc o anidr t se deriuqer to iceps fy t eh motion of a

sy mets ynata i atsn n ksit n foF.O.Dsanwo th se y ets m.

)9( S gni le ged r ffoee re mode sys :met

T eh s metsy nwohs ni t sih erugif si w tah si kno nw sa a S elgni eergeD of deerF om s sy tem .

eW esu t eh t mre eerged of deerf om to r efer to eht rebmun of c oo anidr t se t tah era deriuqer ot

yficeps yletelpmoc t eh arugifnoc t noi of t eh s sy t .me ,ereH fi t eh po is tion of t eh ssam of t eh

s sy t me si sp deifice t neh cca o ylgnidr t eh po is tion of t eh ps r gni dna da r epm era a osl nedi t deifi .

suhT ew deen tsuj o en oc o anidr te (t tah of t eh )ssam ot yficeps t eh s sy t me comp el t yle dna ecneh

i ksit n sasanwo i gn l foeergede f modeer sy ets m.

gedowT)01( r ee ffo r modee sys :met

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A t ow eerged of deerf om s sy t me With re ecneref to tua omo elib pa p acil tio ,sn t sih si re derref

sa rauq t racre m .ledo ttobehT o sreferssamm t ssamo o eleehw,elxaf t cc o pm o nen t erahcihws

leb ow t eh su isneps on ps r gni a dn t eh top ma ss srefer to t eh ssam of t eh portion of t eh rac a dn

pas es nger. ecniS ew deen to yficeps b to h t eh top dna ttob om am ss po is tio sn to comp el t yle

sehtyficeps y ets m ocebsiht, m tase w edo g foeer f modeer sy ets m .

biVfosepyT)11( r ota ry m ito o :n

T)21( y biVfosep r :noita

gnoL)a( i idut n vla i tarb i no arT)b( nsv tarbiVesre i no sroT)c( ion la Vi tarb ion .

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L)31( o gn i biVlanidut r :noita

nehW t eh rap t selci of t eh hs a tf or csid sevom para lell to t eh ax si of t eh hs aft, t neh t eh

vi tarb i ksno n sanwo longi vlanidut i tarb i .sno

F)41( ree adnu mped l bivlanidutigno r ;snoita

nehW a ob dy si dewolla to arbiv te on its o ,nw fa t re gnivig ti na ini t lai mecalpsid ent,

t neh t eh gnirusne arbiv t snoi era kno nw sa eerf or an t ru al arbiv tio .sn nehW t eh arbiv tio sn t ekaecalp lellarap ot t eh sixa of tniartsnoc dna on mad p gni si rp o ,dediv t neh ti si dellac fr ee

depmadnu longi idut n ivla b tar i sno .

aN)51( tur f la r ffoycneuqe r depmadnuee l lanidutigno biv r ita on:

iuqE)a.51( l bi r mmui e odoht r Ne notw s :dohtem

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nE)b.51( er yg M te doh nI eerf arbiv t ,snoi on rene gy si t derrefsnar ni to t eh s sy t me or r f om t eh s sy t .me Th ere f ro e,

EKfomus(ygrenelatoteht semitehtllaemassidnatnatsnocsi)EPdna .

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hgielyaR)c( s ohtem dIn t sih em t ,doh t eh mumixam enik t ci ene rgy ta naem p so ition si edam lauqe to t eh

tnetopmumixam i ygrenela ertxeehtta m sope iti no .

aviuqE)61( l tne s it ff nes fos spr .gni

S)1( pr ni sg in s r e iesS)2( pr ni sg in ap rall le

)3( Combi den rps i sgnI)4( n lc i rpsden in sg

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)71( :gnipmaD

tI si eht ecnatsiser to t eh motion of a arbiv t gni bod .y ehT arbiv t snoi ssa o aic t de iw th t sih

atsiser n keraec n ivdepmadsanwo b tar i sno .

)81( sepyT fo :gnipmad

V)1( i adsuocs mpi gnrD)2( y fri tc i rono c uo lom adb mpi gnloS)3( i pmadd i tcurtsrogn u lar gnipmad

lS)4( i irop n ret f laica gnipmad .

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)91( gnipmaD :tneiciffeoC

adehT m gnip f nurepecro i evt l co ity k si n adsanwo m tneiciffeocgnip .

)02( tnelaviuqE gnipmad :tneiciffeoc

aD m amsrep y edetcennoceb i larapniroseiresnireht l otle vorp i uqered i ipmadder ng.

aD)12( m biVdep r ita on:

vehT i tarb ion cossas i wdeta i htht i keraecnatsisers n nwo tarbivdepmadsa i no s.

aD)22( m gnip fac ot r:

maD p gni caf t ro nac eb denifed sa t eh rat oi of ca t lau da gnipm oc e iff c tnei ot irc t ci al

ad mpi ciffeocgn ient .

5056EM:edoCbuS


adehT m gnip f nurepecro i evt l co ity k si n adsanwo m tneiciffeocgnip .








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adehT m gnip f nurepecro i evt l co ity ksi n adsanwo m tneiciffeocgnip .








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amsuhT i ln y rasesaceerht i epedes n tnognid he v foeula

Wh ne t eh s sy t me u seogredn oirepa d laci ly d ce a gniy om tion dna ecneh hcus s sy te sm era s dia tevO r ad mped metsyS s .

nA e max p el of hcus a s sy tem si a do r o da pm er nehw we o anep door dna ne t re a or o ,m ew wa tn eht ot yllaudarg lc o es ar t reh t nah tibihxe allicso t yro om tion a dn gnab ni to eht nosrep ne t gnire t eh ro mo eb

oS!su adeht m rep i giseds n thcusde h ta

Cr iti c la ly epmad d noitom ( a opyh t laciteh bo enilredr esac es p ara t gni o allics ot ry ced ay rf o

doirep i acedc y acedtsetsafehtI) y tomcidoirepagni i no .

nehW < 1, (x t) si a depmad sunis o di dna t eh ys st ibihxeme t as arbiv to omyr t noi who ilpmaes t edu k

dimini hs ing. sihT si eht tsom co mm on arbiv tion esac a dn ew lliw dneps tsom of o r u t emi stud gniy sy ets ms. otderrefereraesehT sa ednU r ad mped smetsys .

agoL)32( r hti mic decr me e :tn

tI si de denif sa t eh an tur la lo ag rit mh of rat oi of a yn t ow evisseccus ma p il tud se of an

adrednu m sdep y ets m. tI i snemidas i tnauqsselno ity.

W aDenifede m gnip f rotca sa

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T)42( r na s ev rse biV r :noita

tnehW h trape i foselc ahseht f drot i cs m letamixorppasevo y totralucidneprep he xa i os f

th se haf t,t h tne h ive b tar i ksno n snartsanwo v tarbivesre i no s.

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ihW)52( rl psgni ee ahsfod ft:

ehT ,deeps ta hcihw t eh tfahs snur os t tah t eh idda tio lan celfed tion of t eh hs a tf rf om t eh

xa i fos tor ati no b nifnisemoce i ,et i ks n rcsanwo iti lac hwro irl .deepsgni

oN tfahs nac e rev eb ep r cef t yl st thgiar ro cefrep t yl decnalab . nehW na el neme t of mass is a

sid t ecna rf om t eh sixa of or tatio ,n nec t lagufir fo ,ecr w lli t dne ot llup t eh ssam out .draw The

sale t ci rp o rep t sei of t eh s tfah lliw tca ot tser o er t eh arts ightn se s. fI t eh neuqerf cy of or tat noi si

lauqe to o en of t eh r se o tnan seicneuqerf of t eh fahs t, ihw r gnil w lli o .rucc nI o redr ot evas t eh

m hca i en f mor f repo,erulia ati hwhcustano i lr i sdeepsgn m tsu b ae voi .ded

ehT gnilrihw neuqerf cy of a s emmy t cir rc o ss ces t noi of a nevig le gn th eb t neew t ow po ni ts si

ig v bne y:

MPR

erehW E = s'gnuoy ,suludom I = dnoceS mo tnem ,aerafo =m ssam of t eh fahs t, =L le gn th

fo th se haf iopneewtebt n st

ahsA f wt i giewht h ahlliwdeddast v ugnanae l evra l co ity pr(Nfo m elaviuqe) n sat foll :swo

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oT)62( rsio biVlan r :noita

nehW t eh rap t selci of t eh tfahs ro csid mo ev ni a elcric tuoba t eh ax si of t eh shaft, t neh

th ive b tar i ksno n snetsanwo i vlano i tarb i no

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oT)72( r bivlanois r elgnisafonoita r roto sys :met

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oT)82( rs bivlanoi r owtafonoita r roto syst me :

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T)92( orsio lan ly e aviuq le ahstn f :t

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E)03( xam lp e Pr bo el :sm

)1 gnirpsA ssam s metsy sah ps r gni st ssenffi of kN/ dnam a ssam of M gk . tI sah t eh an t ru al

qerf u ne cy f o biv rat noi as 21 .zH nA xe t ar 2 gk ssam si coup del to M dna t eh an t ru al neuqerf cy

re bsecud y 2 H .z iF n td he val oseu f dnak M.

)2 A st deppe tfahs fo 50.0 m ni d emai t re rof t eh tsrif 6.0 m gnel t ,h 80.0 m d emai t re for t eh txen

8.1 m dna 30.0 m d emai t re for t eh re iam n gni 0. 52 m gnel t .h elihW t eh 0. 50 m d emai t re dne si,dexif t eh 30.0 m d r etemai dne of t eh hs a tf rac r sei a rotor of ssam mo em nt o r enif t ai 7.41 kg-m

2.

01x38.0silairetamtfahsehtfoyticitsalefosuludomehtfI11

m/N2

foycneuqerflarutanehtdnif,

srot i lano tallicso i ,sno n itcelge n ehtg i tren i fotceffea seht haf .t

)3 . eB t saneew o dil ssam o 01f ehtdnagk roolf tpekera t sbalsow o sif o an,srotal t rebburlaru a dn

,tlef ni .seires ehT an t laru ru r ebb bals sah a st ssenffi of 0003 N/m dna an tnelaviuqe ocsiv us

gnipmad oc e tneiciff of 001 ces.N / .m ehT tlef bals sah a st enffi ss of 00021 N/m dna tnelaviuqe

suocsiv gnipmad oc e iciff e tn of 033 s.N ec/ .m eD ter enim t eh u depmadn a dn t eh mad p de an tur la

f sehtfoseicneuqer y trevnimets i dlac i tcer i itcelgen,no n tg he m osifossa l .srota

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DNI EX

NU ITIVFORCEDVIBR TA I SNO

tnI)1( r itcudo on

)2( Ca su esres ecnano

)3( For dec biv r noita fo as gni le eerged - fo -fr modee sys met

)4( S ydaet etatS eR s snop e ud e ot aH rm ino c licsO l ita on

)5( For dec biv r noita htiw gnipmad

)6( Rota gnit abnu l na cefor dec biv r noita

)7( biV r noita Isol noita dna Tr sna m ibissi l yti

)8( biV r noita Isol srota

)9( esnopseR tuohtiw gnipmad


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TINU - VI DECROF NOITARBIV


nehW a s sy t me si su cejb t de noc t ylsuouni to t emi av r gniy d si t ,secnabru t eh

arbiv t snoi luser t gni u redn t eh erp s ecne of t eh ext lanre d si t bru a ecn a er re erref d to sa fo decrvi tarb i sno .

For dec biv r noita si w neh na la t anre t gni fo ecr or motion si pa p deil to a

m slacinahce y ets m. tsihtfoselpmaxE y oteudenihcamgnihsawgnikahsaedulcninoitarbivfoepna ,ecnalabmi t psnar ortat noi arbiv tion ac( u des yb t kcur ,enigne ,sgnirps ro ,da et ,)c ro t eh

noitarbiv o af gnidliub ud r nagni rae t ekauqh . nI arbivdecrof t ehtnoi qerf u ne cy of t eh arbiv t noi sit eh neuqerf cy of t eh fo ecr or om tion pa p ,deil iw th o r edr of ingam t edu gnieb ped e dn e tn on t eh

lautca m lacinahce sys et m .

nehW a elcihev mo sev on a ro hgu ro ,da ti si cont uni o ylsu cejbus t de ot ro daaludnu t gnisuacsnoi t eh sys t otme etarbiv ,hctip( ,ecnuob ellor t )c . suhT t eh tua o elibom si dias to

ogrednu decrof .snoitarbiv alimiS r yl revenehw eht enigne si t denru o ,n t ereh si a luser ta tnlaudiser u ecnalabn fo ecr t tah si t imsnar tt de ot eht c sissah of t eh elcihev t rh o hgu t eh e enign

,stnuom gnisuac niaga decrof arbiv t snoi ehtfo elcihev on its .sissahc A gnidliub nehw su cejb t de

ot emit av r gniy dnuorg om t noi )ekauqhtrae( or dniw ,sdaol seogrednu decrof arbiv tio .sn Th sum arpehtfotso cti lac foselpmaxe tarbiv ion deednieras f tarbivdecro ions.

C)2( a su es res cnano e:

ecnanoseR si elpmis to srednu t dna fi you weiv t eh ps r gni dna ma ss sa e ren gy s ot egar

stnemele iw th t eh ssam st gniro k eni t ci rene gy dna t eh gnirps sto gnir pot ne t lai e ren gy. Asd sucsi s de ,reilrae nehw t eh ssam dna gnirps evah on ecrof ca t gni on t meh t yeh t nar s ref rene gy

kcab dna forth ta a ar te lauqe to t eh an t laru fre neuq c .y nI rehto wo ,sdr fi rene gy si ot ebneiciffe t otnidepmupyl gnirpsdnassamehthtob t reneeh g sdeenecruosy to deef t taniygreneeh

a ar te lauqe to t eh an t laru fr neuqe c .y ppA l gniy a fo ecr ot t eh ssam a dn ps r gni si ralimis to

gnihsup a dlihc on ,gniws uoy deen to hsup ta t eh co tcerr tnemom fi you tnaw t eh sw gni to tegrehgih dna .rehgih sA ni t eh esac of t eh ,gniws t eh fo ecr deilppa do se ton secen sar yli evah to eb

gothgih et l egra m to i sehsupeht;sno j otdeentsu k iddapee n eg n gre y i totn h se y ets m .

T eh ,repmad daetsni of gnirots rene g ,y setapissid rene g .y ecniS t eh gnipmad fo ecr si

lanoitroporp to eht icolev t ,y eht erom t eh om t ,noi t eh mo er t eh repmad d apissi t se t eh e ren g .yrehT e erof a po tni w lli co em w neh t eh e ren gy d apissi t de yb ht e da r epm w lli qe ual t eh rene gy

gnieb def ni yb eht fo .ecr tA siht po ni t, t eh s sy t me sah dehcaer its mixam um a ilpm t edu dna willeunitnoc ot etarbiv ta t sih level sa lo gn sa t eh fo ecr pa p deil st sya t eh .emas fI on gnipmad sixe t ,s

t ereh si on t gnih to d apissi te t eh rene gy a dn t reh efo er t eh o er t yllaci t eh mot noi w lli cont euni toworg ino n ot in if nity.

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)3( For bivdec r gnisafonoita le eerged -of-fr modee sys :met

eW was t tah nehw a s sy t me si nevig na ini t lai tupni o renef g ,y eit r eh ni t eh form

fo na ini t lai d si p tnemecal ro na ini t lai olev cit ,y dna t neh re desael ti w ,lli u redn t eh r thgi,snoitidnoc etarbiv .yleerf If t ereh si gnipmad ni eht s sy t ,me t neh t eh o allics tio sn d ei yawa . If a

s sy t me si nevig a cont suouni tupni of e r en gy ni t eh form of a noc t suouni ly pa p deil for ec or aylsuounitnoc deilppa ,tnemecalpsid neht t eh co tneuqesn arbiv tion si dellac fo decr arbiv tio .n ehT

rene gy tupni nac crevo o em t tah apissid t de yb d ma p gni inahcem s sm dna t eh o allics tio sn erasus at ined.

eW lliw redisnoc t ow t sepy of decrof biv rat .noi ehT tsrif si erehw eht dnuorg otsehthcihw y dehcattasimets is i repagniogrednuflest i do i tarbivehtsahcus,tnemecalpsidc i fono

a b iu l nid g .ekauqhtraenani dnocesehT i repaerehws i do ic f ecro i ehtotdeilppas m boro,ssa j tce

;noitomehtgnimrofrep ehtybracafoydobehtnodetrexesecrofehtebthgimelpmaxena secrofrp o decud ni t eh .enigne T tselpmiseh of rm o epf r cidoi roecrof tnemecalpsid si nis uso ,ladi os ew

lliw nigeb by isnoc d gnire fo decr arbiv t noi due to s suni o ladi motion of eht rg o .dnu nI a ll real

s ,smetsy rene g lliwy eb d ,detapissi e.i . t eh s sy t lliwme ,depmadeb tub oft ne t eh da gnipm si ev ry

small f suteloS. i lanatsr y sez y erehthcihwnismets i adons m .gnip

( ydaetS)4 tatS e eR s snop e ud e ot aH rm ino c licsO l ita o :n

Con r psaredis i gn -m ssa - srepmad y ssamets h 1.4erugifninwo . Th tauqee i fono

m to i ssihtfono y rahaotdetcejbusmets m cino f ecro nac b ge i bnev y

(4 )1.

wh ,ere m, kand c addnassenffitsgnirps,ssamehtera m feocgnip f sehtfotneici y ets m, Fi ts helpma i ,ecrofehtfoedut w tsi h cxee i tat i no f cneuqer y virdro i gn f cneuqer y.

raH1.4erugiF m cxeyllacino i sdet y mets

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ecroF:2.4erugiF p lo y nog

ehT st ae dy state pser o esn of t eh s sy t me nac eb ed t denimre yb so gnivl auqe tio )1.4(n ni am ny

tnereffid syaw . ereH a relpmis lacihparg em t doh si desu w hcih w lli evig p lacisyh u edn rst na d gniot t sih d cimany rp o .melb rF o sm o ul t noi of d nereffi t auqelai tio sn ti si kno nw t tah t eh st ydae state

tulos i trap(no i argetniraluc l ehtfoeblliw) f mro

(4 )2.

sA hcae term of auqe t noi )1.4( neserper ts a forc gni term ,.ziv if rst, ces o dn a dn t drih ter ,smtneserper eht reni t ai fo ,ecr gnirps fo ,ecr dna eht d gnipma fo .secr ehT t mre ni t eh rig th dnah s edi

of auqe tion )1.4( si t eh pa p deil fo .ecr enO may ward a lc o es po nogyl sa hs o nw ni erugif 2.4edisnoc r gni t eh qe u bili r mui of t eh s sy tem u r edn t eh ca tion of t eseh fo .secr gniredisnoC a

erefer n lec i ten h ese f eserpebnacsecro n sadet f .swollo

gnirpS ecrof = sihT( fo ecr lliw ekam na elgna htiw eht

er f ere n lec i eserper,en n bdet y li Oen A .)

gnipmaD ecrof = sihT( ecrof lliw eb ralucidneprep ot t eh ps r gnif eserper,ecro n bdet y enil A .)B

aitrenI ecrof = siht( ecrof si p cidnepre u ral ot eht mad p gnif aecro n sopponisid i det i tcer i wno i tht h irpse ng f aecro n eserpersid n bdet y li )CBen .

deilppA ecrof = hcihw nac eb d nwar ta na elgna htiw tcepser ot eht

er f ere n lec i aen n erpersid sen bdet y li COen .

rF om auqe t noi ,)1( t eh luser t tna of t eh gnirps fo ,ecr gnipmad fo ecr dna t eh reni t ai fo ecr w lli eb th

lppa i de f hw,ecro i lraelcsihc y sh f ninwo i 2.4erug .

tI may eb on t de t tah t lli no ,w ew do t'n wonk ba o tu t eh ingam t edu ofXand nachcihw eb isae l cy o upm t de rf om

iF gure .2 warD ing a li larapDCen l otle AB, f mor th r te iangl f oDCOe F gi ,2eru

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morF verpeht i suo m udo l foe f eer - tarbiv i no it m ebyalacer l tde hat

larutaN f euqer ncy

rC iti lac ad m gnip

aD m gnip f adrorotca m targnip io

eH n ,ec

ro

tsA h re atio tsi h tse ati tcelfedc i no fo th pse ir ng, i k s nown sa

arorotcafnoitacifingameht m sehtfooitaredutilp y mets

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)5( For bivdec r adhtiwnoita m :gnip

vahebehteeslliwewnoitcessihtnI i repmadssamgnirpsehtforuo m ddaewnehwledo

a ah rmo cin fo ecr ni eht f ro m .woleb A fo ecr of t sih t epy ,dluoc rof ,elpmaxe eb areneg t de yb a

tor atin ecnalabmig .

musniagaewfI the f tnosecro h ehttegewssame f lo l ranidrogniwo y ereffid nti tauqela ion:

daetsehT y osetats l tu i fono borpsiht l me rwebnac i :sanett

T eh tluser stat se t tah t eh ssam lliw o allics te ta t eh emas neuqerf c ,y ,f of t eh deilppa fo ,ecr

wtub i ihsesahpaht ft .

tarbivehtfoedutilpmaehT i no X ehtybdenifedsi f lo l gniwo f .alumro

erehW r si de denif sa t eh ar t oi fo t eh mrah o cin ecrof neuqerf cy o r ev t eh u depmadn

n laruta f euqer ncy f o the m ssa rps ing repmad mo led .

,tfihsesahpehT bdenifedsi, y eht f lo l gniwo f .alumro

ehT plot of t eseh fu cn t ,snoi dellac "t eh neuqerf cy esnopser of t eh s sy te ,"m neserp ts o en of t eh

tsom tnatropmi serutaef ni decrof arbiv t .noi nI a ylthgil da depm s sy t me w neh t eh forc gni

qerf u ycne sraen t eh larutan uqerf ency ( ) t eh amp il t edu of t eh arbiv tion nac teg xe t emer ly

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high. sihT p neh o nem on si ca dell r cnanose e neuqesbus( t yl t eh an t ru al neuqerf cy of a s sy tem si

netfo derrefer ot sa t eh tnanoser neuqerf c .)y nI tor or aeb r gni s sy t sme yna rotat lanoi deeps t tah

cxe i oseraset nant f cneuqer y i r casaotderrefers i lacit deeps .

If ecnanoser o srucc ni a em c cinah al s sy t me ti nac eb ev ry ah r fm ul gnidael to

foeruliaflautneve th se y ets m. neuqesnoC t arbivrofsnosaerrojamehtfoeno,yl t otsisisylananoi

erp d tci nehw t sih t epy of ecnanoser may o r ucc dna t neh to ed t enimre w tah st spe ot t eka ot

titneverp .gnirruccomorf edutilpmaehtsA tolp dgnidda,swohs amp gni cifingisnac ant yl r ecude

eht edutingam of t eh arbiv tio .n ,oslA t eh ingam t edu nac eb uder c de fi t eh an t laru qerf uency can

eb fihs t de wa ay r f om t eh fo gnicr fr neuqe cy yb c gnignah t eh st ssenffi or ssam of t eh s sy t .me If

eht s metsy tonnac eb ,degnahc spahrep t eh fo gnicr neuqerf cy nac eb fihs t de (for ,elpmaxe

ch tgnigna h fodeepse the m hca i itarenegen n .)ecrofehtg

ehT fo ll o gniw era so em ot r eh po ni ts ni er g sdra to t eh fo decr arbiv tion ohs wn ni t eh euqerf ncy

esnopser pl to s.

tA a nevig neuqerf cy ar tio, t eh ma p il t edu of t eh arbiv t ,noi X, si cerid t yl rp oportio lan ot

aeht m lp i ehtfoedut f ecro F0 .g.e( fi y buoduo l ehte f tarbiveht,ecro i )selbuodno

iW th il t elt ro on ,gnipmad t eh arbiv tion si ni esahp iw th t eh of r gnic uqerf ency when t eh

tarycneuqerf io r ehtnehwesahpfotuoseerged081dna1< f cneuqer y tar io r> 1

hW en r 1 t eh edutilpma si tsuj t eh celfed tion of t eh ps r gni u redn t eh stat ci

f ecro F0. sihT de celf t noi si dellac t eh stat ci de lf ection st. ,ecneH nehw r1 t eh e ceff ts of t eh

ad m arep n ehtd m erassa mi in mal.

hW en r arbivehtfoedutilpmaeht1 t noitcelfedcitatsehtnahtsselyllautcasinoi st. nI

t sih iger on t eh ecrof areneg t de yb t eh ssam (F= am ) animodsi t gni aceb u es t eh arelecca t neesnoi

yb wsesaercnissameht i cneuqerfehtht y. S ecni t celfedeh t nineesnoi t eh ,gnirps X nidecudersi,

siht iger o ,n t eh ecrof t imsnar tt de yb t eh gnirps (F= kx) ot t eh esab si .decuder eroferehT eht

m sa ss r p ing alosisimetsysrepmad t rfecrofcinomrahehtgni o nuomehtm t gni esab er f otderre

noitarbivsa si o .noital nI t sere t ,ylgni mo er mad p gni ca t lau ly secuder t eh ceffe ts of biv ration

i os l ta i nehwno r adehtesuaceb1 mpi gn f (ecro F= cv lasi) s msnarto i dett tot he bas .e

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R)6( ota abnugnit l ecna for bivdec r :noita

enO may dnif ynam or tat gni s smetsy ni sudni rt lai pa p acil t .snoi T eh u decnalabn

ahcusniecrof s serperebnacmetsy ent aybde ssam mwi rtnecceht ici yt e iwgnitatorsihcihw, than evralug l co ity ssa h Fninwo i 1.4erug .

V:1.4erugiF i itarb n sg y mets wi torht ati nugn b ala n ec

erugiF .2.4 ydobeerF margaid o sehtf y ts em

L te xb te h de i emecalps n fot tornoneht ati (ssamgn M-m ) f mor tatseht ic muirbiliuqe

sop iti gnitatorehtfotnemecalpsidehtneht,no m ssa mis

morF eht f ydobeer margaid sehtfo y mets tauqeeht,2.4erugifninwohs i fono m to i sino

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.4( 1)

or .4( 2)

tauqesihT i no i tauqesaemass i w)1(no h ere F persi l bdeca y . morfoS eht f lopecro y nogssa h nwo in fig r u e 3.4

.4( 3)

or .4( 4)

ro ( )5.4

Fi :3.4erug opecroF ly nog

ro (4.6)

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a dn (4.7)

toS h oce m osetelp l tu i no b oce m se

(4.8)

biV)7( r Inoita sol dnanoita Tr sna m ibissi l :yti

nehW a enihcam si ,gnitarepo ti si detcejbus ot lareves t emi av r gniy fo secr esuaceb of ihw

sdnet ot tibihxe arbiv t .snoi nI t eh rp o ,ssec so em of t eseh fo secr era t imsnar tt de ot t eh fo adnu tion wdluoc u enimredn t eh efil of t eh adnuof t noi dna osla tceffa t eh o arep tion of na y ot r eh enihcam on t eh

f uo n tad ion. ecneH ti si of tseretni ot eziminim siht fo ecr t issimsnar o .n alimiS r yl w neh a s sy t me si s ejbu

ot dnuorg om tio ,n trap of t eh rg o dnu motion si t imsnar tt de ot t eh s sy tem sa ew tsuj d csi u dess g.e tua omo elib go gni on na u neven ro ;da na sni tru tnem mo nu t de on t eh arbiv t gni sur ecaf of an air tfarc et

eseht ,sesac ew hsiw ot im n ezimi t eh motion t imsnar tt de rf om t eh dnuorg to t eh s sy t .me aredisnochcuSera desu ni t eh ngised of enihcam adnuof tio sn a dn ni o redr ot srednu t dna so em of t eh ba cis seussi vni o

dutslliwew y siht borp l me b nodesa th se in f.o.delg m dledo i osdessucs f .ra

gew e tt h sserpxee i no f ro f msnartecro i totdett he b saesa foll :swo

biV)8( r Inoita sol :srota

Consider a vibrating machine; bolted to a rigid floor (Fig ru e 2 )a .The fo cr e transmitted to the

roolf si lauqe ot eht ecrof detareneg ni eht .enihcam ehT dettimsnart ecrof nac eb desaerced ybgnidda a noisnepsus dna gnipmad stnemele netfo( dellac noitarbiv )srotalosi erugiF b2 , ro yb

gnidda tahw si dellac na aitreni ,kcolb a egral ssam yllausu( a kcolb fo tsac ,)etercnoc yltcerid

dehcatta ot eht enihcam erugiF( rehtonA.)c2 noitpo si ot dda na lanoitidda level fo ssam

(sometimes called a seismic m sa s, again a block fo c sa t concrete) and suspensi no (Figure 2d).

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a dn (4.7)


(4.8)















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e 666888 ooofff 999111


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a dn (4.7)


(4.8)















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Figure 2.Vibration isolation systems: a) Machine bolted to a rigid foundation

b) Support ed on iso al t ion spri sgn , r ig id fo u nd at io n c ) m ca hine a tt ached to anin re t ial block. d) Su pp orted on isolat ion spri gn s, n no -rigid foundation (such as a

floor); or machine on isolation sprin sg , seismic mass and second level of isolatorsprings

nehW o allics t yro secrof esira u van o badi ly ni senihcam ti si u laus ly ed s eri d ot

tneverp eseht secrof rf om gnieb t imsnar t det ot eht .sgnidnuorrus roF ,elpmaxe emos u decnalabn

tidna,enigneracanielbativenierasecrof ehtotdettimsnartyllohweraesehtfielbatrofmocnusi

rac .ydob T eh su u la so ul tion si to mo tnu t eh so ecru of arbiv t noi on r ps u gn pus p ro ts. iV b tar i no

alosi t adnuofehtotdettimsnartecrofronoitomehtfosmretniderusaemsinoi t .noi The l tresse he

f roecro m msnartnoito i ergehtdett a tarbivehtret i osino l ta i no

ppuS o es t tah t eh adnuof tion si ceffe t ylevi r digi a dn t tah o yln o en d ceri tion of

mo tnemev si ceffe t ylevi icxe t de os t tah t eh s sy t me c na eb tr ae t de sa gnivah only o en d eerge of

f odeer m.

nopseR)9( s tiwe h dtuo a ipm n :g

T eh ilpma tude of t eh ecrof imsnart tt de ot t eh adnuof tio sn si erehW k si t eh St ssenffi

fo oppuseht r at ndx( )t i ts h emecalpside n fot the m ssa m .tauqegninrevogehT i bdenimretedebnacno y snoc i latotehttahtgnired f ehtnognicro m sienihca

lauqe ot i st m ssa mul ybdeilpit i tareleccast i notweN(no s s oce nd al )w

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E)01( xam orPelp b el m :s

)1 A ssam o 01f gk si dednepsus rf om o en dne of a lacileh ps r ,gni t eh ot r eh ne d gnieb .dexif The

ssenffits o ehtf gnirps si 01 N/ mm . T eh csiv o dsu amp gni c sua es t eh ma p il t edu to esaerced to o en

htnet fo eht ini t lai eulav ni ruof co elpm te o allics tio .sn If a ep ri do ci of r ec of 051 cos 05 t N si

deilppa ta eht ssam ni eht rev t laci id r ce t ,noi dnif eht ilpma t edu of t eh fo decr arbiv tio .sn tahW si

i st v ertaeula s ano n ?ec

)2 A enihcam roppus t de s emmy tr laci ly on fo r u sgnirps sah a ssam of 08 .gk ehT ssam of t eh

rpicer o ac t gni rap ts si 2 .2 gk hcihw mo ev t rh o hgu a rev t laci stro ek of 001 mm with s elpmi

rah m cino m to i .no celgeN t madgni p ed,gni t enimre t sdenibmoceh t ssenffi of t seh pr osgni t tah t eh

ecrof dettimsnart ot adnuof tion si 2/1 0ht

of t eh sesserpmi fo .ecr ehT enihcam knarc tfahs or tates

008ta pr m.

fI u redn wo gnikr conditio ,sn t eh gnipmad secuder t eh ilpma t sedu of su evissecc arbiv t snoi by

,%03 dnif ( )i t eh fo ecr t imsnar tt de to eht adnuof t noi ta ecnanoser a dn ( )ii t eh ma p il t edu of

vi tarb i no oserta nan .ec

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DNI EX

UNIT-V EM CH NA ISMF RO CONTROL

)1( tnI r udo c it on

)2( Pr picni le fo oW rk gni

)3( Cl issa f itaci on fo vog er on rs

)4( thgieH fo evog r ron

)5( Sl vee elift

)6( Isochr msino

)7( ibatS l yti

(8) gnitnuH

(9) senevitisneS s

)01( ahC r etca r itsi cs dna auq l iti es fo tnec rif lagu evog r ron

)11( ttaW evog r ron

)21( Por ret evog r ron

)31( Pr eo ll evog r ron

41( ) aH r llent evog r ron

51( ) aH r gnut evog r ron

61( ) iW ls no aH r nt e ll evog r ron

)71( P ekci r gni evog r ron

81( ) iD ff ere cn ebe neewt afl leehwy dna a evog r ron

91( )Gyros epoc

02( ) eD scr noitpi dna gaid r ma

)12( tceffE fo eht cipocsoryG elpuoC no na oreA enalp

( 22 )E ff ectofgyroscopiccouple

32( )Eff tce fo yg rosc ipo c lpuoc e no pihs

2( 4) fE f ce t of Gyrosc ipo c Couple on a N va al ihS p ud ring pitching

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2( 5) Eff ce t of Gyrosc ipo c couple on a N ava l hS ip during R illo ng

(26) Eff ce t of Gyroscopic couple on a 4 -wheel drive

2( 7)Exam lp ePr bo l sme

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UNIT- V MECHANISM F RO C NO TR LO

G vo ern ro

tnI)1( r udo c it o :n

A tnec r lagufi evog r ron is a ps e fic ci ty ep o ronrevogf t tah oc n ort ls t deepseh ofybenignena aluger t gni t eh tnuoma (leuffo or gnikrow )diulf timda t ,de os sa ot niam t nia a raen

tnatsnoc deeps revetahw eht rodaol leuf ylppus idnoc t .snoi tI sesu t eh pr icni p el o rpf oportional

oc n ort l .

tI si mo ts o ylsuoivb nees o sn t mae senigne w ereh ti ger u al t se t eh ad issim on of st mae ni to

ceht y .)s(rednil tI si osla fo dnu on ni t lanre co subm tion dnasenigne suoirav ly delleuf t ,senibruand i emosn m rtsnredo i gnik cl skco .

)2( Pr lpicni e roWfo k :gni

Po rew si deilppus to t eh go r onrev rf om t eh e s'enign out tup hs a tf by ( ni t sih)ecnatsni a tleb ro niahc ( ton hs o )nw cennoc t de ot t eh lo r ew tleb w eh e .l T eh nrevog or si

otdetcennoc tahtevlavelttorhta ehtsetaluger lf ow o gnikrowf )maets(diulf gniylppus peht r emiemirp(revom revom ton .)nwohs sA eht deeps of t eh pr emi mo r ev ,sesaercni t eh nec t lar sp ni d el

of t eh go nrev or or tat se ta a saf t re ar te dna t eh k eni t ci rene gy of t eh sllab ercni a .ses sihT swollaeht t ow sessam on r evel smra to evom uo t sdraw dna sdrawpu ga a tsni gr iva t .y If t eh om tio gn o se

raf ,hguone t sih m to noi sesuac t eh revel smra to pu ll do nw on a t surh t ,gniraeb w hcih mo sev amaeb ,egaknil hcihw secuder t eh repa t eru of a t torh t el .evlav ehT ar te of work gni - diulf ne t gnire

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t eh c rednily si t suh decuder dna t eh deeps of t eh pr emi mo r ev si contro ,dell neverp t gni o revs deep ing.

lacinahceM s ot sp yam eb desu ot timil t eh egnar of t torh t el om t ,noi sa seen raen t ehm tnisessa h ie m rtaega ight .

T eh d ri ect noi of t eh revel mra ho gnidl t eh ssam lliw eb alo gn t eh cev tor mus ofitcaereht ve ec n agufirt l f tdnarotcevecro h varge i tat i lano f .ecro

C)3( l sa sif itaci o evogfon r on r :s

Gov r e n cerasro l abdeifissa s tnopude w fido f ere n rpt ni ci selp .

These ar :e

1. eC n irt f lagu og v re n sro

2. Inerti oga v re n sro

lagufirtneC og v erasronre f tru h cre l sadeifissa

vogfothgieH)4( er ron

tI si eht rev t laci d si t ecna eb t neew t eh nec t er of t eh go nrev or sllah dna t eh po tni ofni t cesre t noi eb t neew t eh pu p re ar sm on t eh sixa of sp ni d el si known sa go ev rnor hgieh t. tI sieg n llare y ed n bdeto y h.

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S)5( l vee e lift

ehT v tre i atsidlac n tec h eelse v arte v coteudsle han tnieg h liuqee i muirbdeepS i sehtdellacs l ee v ile f .t The v lacitre wod n artdraw v le may b r ete m sade

eN g ta iv le ift

I)6( sochr msino

T sih si na xe t emer esac of isnes t .ssenevi nehW t eh qe u muirbili deeps si co sn t tna for a ll ar diiof or tat noi of t eh sllab wit nih t eh work gni ,egnar eht go nrev or si dias ot eb ni rhcosi o in s .m T sih

snaem taht t eh reffid e ecn eb t neew t eh mixam um dna muminim qe u irbili um eeps ds si orez dnath snese i evit n llahssse b nifnie i et .

)7( ytilibatS

ilibatS ty si t eh iliba ty ot niatniam a derised enigne deeps iw tho tu culF t au t .gni libatsnI ity

stluser ni nuh t gni or allicso t gni eud to o r ev corr ce tio .n evissecxE st iliba ty ser ults ni a dead- taebseodtahtenororonrevog n to c eiciffustcerro n lt y rof l cdao h segna

)8( H gnitnu

T eh p neh o nem on o cf ont suouni culf t au t noi of t eh enigne deeps a evob a dn leb ow t eh naem

s deep is ret m de as hunt ni g. hT is o srucc in ov r e - isnes t evi orsuonorhcosi sronrevog . esoppuS na suonorhcosi go r onrev si if tt de to na enigne ru gninn ta a

ydaets l .dao iW t thgilsah esaercni o llaflliwdeepseht,daolf dna t lliweveelseh emmi d ai t yle af ll

ot tsewolsti isop t .noi sihT s llah o nep t eh contro evlavl w edi a dn e ssecx ylppus of r ene gy w lli eb,nevig iw th t eh re tlus t tah t eh eps ed w lli ar p yldi ercni a es a dn t eh eveels w lli r esi to its ih gher

sop iti .no sA a resu tl of t sih vom e tnem of t eh els e ,ev t eh control va evl w li l eb tuc o ;ff t eh pus plydnaenigneehtot t eh deeps niagalliw ,llaf t eh c elcy gnieb aeper t de dni e if nit .yle uS ch a go ev rnor

dluow timda ie t reh mo er ro ssel ma uo tn of leuf dna os e tceff wo dlu eb t tah t eh enigne wo dluhun .t

)9( ssenevitisneS

ronrevogA i ass i snesebotd i fi,evit i sdeepsfoegnahcst f onmor L dao ot f llu l dao may eballamssa f tcar i fono the m liuqenae i rb i bissopsadeepsmu l opserrocehtdnae n id n eelsg v ile ft

may b sae l ssopsaegra ibl .eppuS o es

=1 max. iuqE li muirb s deep =2 m ni . liuqe i rb i mu s deep

= m iliuqenae b muir s (=deep +1 2 2/)erehT f snesero i it v (=ssene 1- /)2 2

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ahC)01( racter auqdnascitsi l iti e tnecfos rif voglagu er :ron

tasroF i rotcafs y rep f amro n aec n krowd in lagufirtnecag og v re n sro h uo l ssessopdehT f lo l lauqgniwo i .seit

a. erneddusehtnO m folavo l dao i uohseveelsst l potehttahcaerd m soptso iti Otano n ec .b. opserstI n totes h ce han f oeg sdeeps h uo ld be f tsa .

c. sstI l uohsevee l fd l tatao s emo retni m sopetaide iti r onrednuno m dnoCgnitarepola iti .snod. A ehtt l soptsewo iti f ono eels v senigneehte h eddluo vel po m mumixa rewop .

e. stI h uo ld h tos,rewoptneiciffuseva h ta it may ttrexeotelbaeb h uqere i der f ecroA repooteveelsehtt a et th oce ntr lo & m nahce i ms

vogttaW)11( er on r:

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oP)21( r evogret r on r:

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P)31( r evoglleo r on r:

aH)41( r ent l evogl r on r:

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aH)51( r evoggnut r on r:

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aHnosliW)61( r llent evog r on r:

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)71( P ekci r evoggni r on r:

iD)81( ff nere ec be aneewt fl hwy e evogadnale r on r:

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