Quality Improvement of Unbalanced Three-phase Voltages Rectification

Size: px
Start display at page:

Download "Quality Improvement of Unbalanced Three-phase Voltages Rectification"

Transcription

1 SEI 9 5 h Inrnionl Confrn: Ss of Elroni, hnologis of Inforion nd louniions Mrh -6, 9 UNISIA Quliy Ipron of Unlnd hr-phs ols Rifiion Fi Zhr AMAOUL *, Musph.RAOUFI * nd Mouly hr LAMCHICH * * Dprn of physis, Fuly of Ss Slli Unirsiy Cdi Ayyd P.O. BOX 9, Mrrksh, Moroo fz.oul@u.. roufi@u.. lhih@u.. Asr: In his ppr w r h s whr unln is on h ll of h powr supply, nd prsn hod o opns his unln of h nwork. his hod is sd on onsidrg gnrl hr phs ols of unqul pliud nd rirry phs. his ol sys is hn oposd wo squns: posii nd ngi squn. h zro squn is ssurd o zro. For h squn, odulion swihg funion is drd. h ol h d sid is hn xprssd s funion of wo squns ol, nd h rld swihg. In h o DC ol xprssion, hr r rs h gnr hronis, w k hoi h h su of hroni rs quls zro. A glol swihg funion is hn drd. Ky words: PMW rifir, unln ol, uni powr for (UPF). INRODUCION h lril nwork sud o n nironn so i sr, is h s of idns whih us disurns of h powr supply du gnrl o syris of dns of h ls of h nwork, wih h rious ffs of shor-irui of origs ffg h nwork, wih h unln of h sour, h srong sgl-phs lods or d disriuion of h lods on h lril nwork. Whn suh df ours, hr is irh of non syry of orn ol whih n ndngr h sfy of h popl nd drior h xisg sllions h lril nwork, if i is no quikly lid [CHE 6]. his ppr proposs nw onrol sh for h /d hr-ll PWM rifir undr gnrlizd unlnd oprg ondiions. h qunifiion of his unln is sd on h ols doposiion ordg o h syril oponn of Forsu [GRA ]. his hod pris o spr h hrphs unlnd ols on hr lnd dpndn syss known s dir (posii squn), opposi (ngi squn) nd hoopolr. Siulion ws ondud undr wo diffrn ss of unlnd oprg ondiions. h firs s is 9% unln on phs pu ol. h sond unln s is doul susoidl pu. his sond unln s is on xpl of h xr unlnd oprg ondiions. his priulr oprg ondiion is lso oonly found rsidnil rs whr oh nd pu ols r ill [SUH ]. A dild siulion progr is prprd y usg Ml/Siulk. Siulion nd xprl rsuls onfir h proposd onrol hod. Figur. PWM /d onrr undr gnrlisd unlnd oprg ondiions. - -

2 SEI Rifir wih ouion ford wih sour of unln ol: opnsion of unln Considrg hr-phs pu ols (unqul pliuds nd rirry phss) wihou zro squn s h orhogonl su of posii nd ngi squn, hrfor h pu n wri h nry lik or of hr lns: i () Aordg o h quion of Eulr, h ol of phs n rprsnd y h su of wo oplx sizs, for xpl, for phs : () () (5) nd r rspily h phsor of pliud nd his od oplx. (6) (7) h s forlis is pplid o ohr phss. h sp phsor of h hr-phs sys n xprssd s: i (8) i (9) W noi h h nsion i is oposd of posii squn nd ngi squn of ol. h posii squn is dfd s: p R () p R () hrfor, h hr ols of h posii squn r wr: p p p Wih h s nnr, h ngi squn is: n R Fro whr h hr ols of h ngi squn r wr: n n n And h oupu ol onuous sid n dsrid wih h followg quion: d (5) Whr, r h swihg funions rli o h hr rs of h PWM rifir, whih n k h lu () or (-), quion (6) n wr oril for: d (6) h firs wo rs produ h onsn ol d, whil h wo ohr rs produ hroni h frquny of h l. [GRA ] If h nsions of h posii squn r wr: p p p p p p p p p (7) h orrspondg swihg funions r hn () () () ()

3 SEI9 p p p p p p p p p Wh produs: p p Afr lulion, w fd: ( ) (8) (9) () p p h s nnr for h ngi squn, if w k s xpl: n n n n n n n ( ) n n n n n And ( ) n n p n n n W fd: ( ) () () () n p n () n p If hs quniis r srd o forul (9), h ls wo rs i yilds: ( ) p p If w hoos: p n (5) (6) p n hus h wo undsirl rs r nlld wn h. And h forul (9) os: (8) d n d p p p (9) hrfor, h funion of odulion whih pris o produ onuous nd onsn ol for ny ondiion usg n unln is: () i p i ( ) p W no h only h pliud of h posii squn pprs h xprssion (), whih p n surd y filrg. h xprssion () is usd o dlop h dir of h l lok of h Fig.. Non-syry ol is hrrizd y is dgr whih is dfd y usg h hod of h oponns of Forsu y h opposi h rio of h pliuds of h rs nd dir ol [CHE 6], hrfor h for of non-syry or unln is dfd y h followg rlionsh: U n () p hn quion () os: ( U ) ( ) () d p p hrfor, h xprssion of h xiu lu of h ol is: d ( ) () U () d p Equion () shows h rlionsh wn h onuous ol nd h for of unln, s long s his ls rss, whih dus rduion on h ll of d ol nd rrolly. h Fig. shows h oluion of h xiu lu of h ol d ordg o h for of unln. hn (7) - -

4 SEI9 L,, L L R, R, R Dphsg of 9 * s ο s( ) ο s( ) l..prrs usd siulion for s Dphsg of 9 * Fig. illusrs h hr phs ols, whr h ol hs n unln of 9% h pliud, Fig. shows h phs () pu urrn, nd h phs () pu ol, flly, Fig. illusrs h onrr oupu d ol. Dphsg of 9 p Figur. Modulion wih orrion of unln. d p * 5 6 hr Ls phs rois nsion ols du résu (), (), (), () () ps(s) i (s) () Figur. ol unl. U (%) d ordg o h for of. Siulion Rsuls nd disussions o pro h fsiiliy nd h prforn of h proposd onrol sh undr rious gnrlizd unln oprg ondiions, siulion ws d for wo diffrn unlnd oprg ondiions. Cs I: 9% of unln on phs pu ol his kd of unlnd pu ondiion is qui oon wk sys [SUH ]. h prrs of our sys for his ondiion r surizd l. ol nsion nd ourn urrn d of phs () (), I (A) I () ol DC() nsion d() I ps(s) i (s) () ps(s) i (s) () - -

5 SEI9 8 ol nsion DC() d() ps(s) i (s) (d) Ls rois nsions du résu (), (), () hr hr phs phs ols ols (), (), (), (), () () ps(s) i (s) () Figur. Rsuls of siulion h s of 9% of unln on h ll of h pliud : () hr phs ols; () ol of h phs (); () urrn of h phs (); (d) DC ol. Aordg o Fig., w s h h urrn is prilly susoidl nd phs wih h ol of h phs (). Fig. shows h h d ol follows is rfrn. Cs II: A doul susoidl pu Alhough his yp of unlnd oprg ondiion is no s oon s h of s, doul susoidl pu is onsidrd o on of h os xr unlnd oprg ondiions. Consqunly, i is suil xpl o x h prforn piliy of proposd hod. h sys prrs of his ondiion r rpiuld l. nsion ourn d () I(A) ol nd urrn of phs (), I () ol nsion d() DC() I ps(s) i (s) () s ο s( ) l. Prrs usd siulion for s Fig. prsns h hr ols, Fig. illusrs h ol nd h urrn of h phs (), w s h h urrn is prilly susoidl nd phs wih h ol, flly h Fig. shows h h ol follows is rfrn u wih h prsn of h rpl. ol nsion DC() d() ps(s) i (s) () ps(s) i (s) (d) Figur 5. Rsuls of siulion h s of u on h ll of h hird phs: () hr phs ols; () ol of h phs (); () urrn of h phs (); (d) DC ol

6 SEI9 Figur 6. Siulk odl usd for h opnsion of unln. Figur 7. Blok of opnsion of unlund pu ols.. Conlusion his ppr proposs nw hod for hr-ll PWM rifir oprg undr gnrlizd unlnd oprg ondiions. An xr unlnd oprg ondiion of pu ol s on of wo xpl ondiions for h siulion his ppr. h d oupu nd nrly uniy powr for sid of h rifir show h ffss of h hod. REFERENCES [FE 6] CHERIF FEHA, "nlys éliorion d l di d l non-syéri d nsion dns l qulié d l énrgi élriqu", hès d Door d E, Unirsié d Bn, Fulé ds Ss d l géniur, pp., pp., Mi 6. [GRA ] D.Grh Hols, hos A.Lo, "Puls Wih Modulion for Powr Conrrs : Prls nd Pri", pp.-5, -, , IEEE Copur Soiy Prss, Oor. [SUH ] Y.Suh,. irs,. A. Lo, "A Nonlr Conrol of h Insnnous Powr dq Synhronous Fr for PWM AC/DC Conrr undr Gnrlizd unlnd Oprg Condiions", Unirsiy of Wisons- Mdison ol, oor

A Study of the Solutions of the Lotka Volterra. Prey Predator System Using Perturbation. Technique

A Study of the Solutions of the Lotka Volterra. Prey Predator System Using Perturbation. Technique Inrnionl hmil orum no. 667-67 Sud of h Soluions of h o Volrr r rdor Ssm Using rurion Thniqu D.Vnu ol Ro * D. of lid hmis IT Collg of Sin IT Univrsi Vishnm.. Indi Y... Thorni D. of lid hmis IT Collg of

More information

Single Correct Type. cos z + k, then the value of k equals. dx = 2 dz. (a) 1 (b) 0 (c)1 (d) 2 (code-v2t3paq10) l (c) ( l ) x.

Single Correct Type. cos z + k, then the value of k equals. dx = 2 dz. (a) 1 (b) 0 (c)1 (d) 2 (code-v2t3paq10) l (c) ( l ) x. IIT JEE/AIEEE MATHS y SUHAAG SIR Bhopl, Ph. (755)3 www.kolsss.om Qusion. & Soluion. In. Cl. Pg: of 6 TOPIC = INTEGRAL CALCULUS Singl Corr Typ 3 3 3 Qu.. L f () = sin + sin + + sin + hn h primiiv of f()

More information

LINEAR 2 nd ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

LINEAR 2 nd ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS Diol Bgyoko (0) I.INTRODUCTION LINEAR d ORDER DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS I. Dfiiio All suh diffril quios s i h sdrd or oil form: y + y + y Q( x) dy d y wih y d y d dx dx whr,, d

More information

3.4 Repeated Roots; Reduction of Order

3.4 Repeated Roots; Reduction of Order 3.4 Rpd Roos; Rducion of Ordr Rcll our nd ordr linr homognous ODE b c 0 whr, b nd c r consns. Assuming n xponnil soluion lds o chrcrisic quion: r r br c 0 Qudric formul or fcoring ilds wo soluions, r &

More information

Major: All Engineering Majors. Authors: Autar Kaw, Luke Snyder

Major: All Engineering Majors. Authors: Autar Kaw, Luke Snyder Nolr Rgrsso Mjor: All Egrg Mjors Auhors: Aur Kw, Luk Sydr hp://urclhodsgusfdu Trsforg Nurcl Mhods Educo for STEM Udrgrdus 3/9/5 hp://urclhodsgusfdu Nolr Rgrsso hp://urclhodsgusfdu Nolr Rgrsso So populr

More information

Revisiting what you have learned in Advanced Mathematical Analysis

Revisiting what you have learned in Advanced Mathematical Analysis Fourir sris Rvisiing wh you hv lrnd in Advncd Mhmicl Anlysis L f x b priodic funcion of priod nd is ingrbl ovr priod. f x cn b rprsnd by rigonomric sris, f x n cos nx bn sin nx n cos x b sin x cosx b whr

More information

Midterm. Answer Key. 1. Give a short explanation of the following terms.

Midterm. Answer Key. 1. Give a short explanation of the following terms. ECO 33-00: on nd Bnking Souhrn hodis Univrsi Spring 008 Tol Poins 00 0 poins for h pr idrm Answr K. Giv shor xplnion of h following rms. Fi mon Fi mon is nrl oslssl produd ommodi h n oslssl sord, oslssl

More information

16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 3: Ideal Nozzle Fluid Mechanics

16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 3: Ideal Nozzle Fluid Mechanics 6.5, Rok ropulsion rof. nul rinz-snhz Lur 3: Idl Nozzl luid hnis Idl Nozzl low wih No Sprion (-D) - Qusi -D (slndr) pproximion - Idl gs ssumd ( ) mu + Opimum xpnsion: - or lss, >, ould driv mor forwrd

More information

On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument

On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument Inrnaional Rsarch Journal of Applid Basic Scincs 03 Aailabl onlin a wwwirjabscom ISSN 5-838X / Vol 4 (): 47-433 Scinc Eplorr Publicaions On h Driais of Bssl Modifid Bssl Funcions wih Rspc o h Ordr h Argumn

More information

On the Existence and uniqueness for solution of system Fractional Differential Equations

On the Existence and uniqueness for solution of system Fractional Differential Equations OSR Jourl o Mhms OSR-JM SSN: 78-578. Volum 4 ssu 3 Nov. - D. PP -5 www.osrjourls.org O h Es d uquss or soluo o ssm rol Drl Equos Mh Ad Al-Wh Dprm o Appld S Uvrs o holog Bghdd- rq Asr: hs ppr w d horm o

More information

Right Angle Trigonometry

Right Angle Trigonometry Righ gl Trigoomry I. si Fs d Dfiiios. Righ gl gl msurig 90. Srigh gl gl msurig 80. u gl gl msurig w 0 d 90 4. omplmry gls wo gls whos sum is 90 5. Supplmry gls wo gls whos sum is 80 6. Righ rigl rigl wih

More information

Inventory Management Model with Quadratic Demand, Variable Holding Cost with Salvage value

Inventory Management Model with Quadratic Demand, Variable Holding Cost with Salvage value Asr Rsr Journl of Mngmn Sins ISSN 9 7 Vol. 8- Jnury Rs. J. Mngmn Si. Invnory Mngmn Modl wi udri Dmnd Vril Holding Cos wi Slvg vlu Mon R. nd Vnkswrlu R. F-Civil Dp of Mmis Collg of Miliry Enginring Pun

More information

Reliability Analysis of a Bridge and Parallel Series Networks with Critical and Non- Critical Human Errors: A Block Diagram Approach.

Reliability Analysis of a Bridge and Parallel Series Networks with Critical and Non- Critical Human Errors: A Block Diagram Approach. Inrnaional Journal of Compuaional Sin and Mahmais. ISSN 97-3189 Volum 3, Numr 3 11, pp. 351-3 Inrnaional Rsarh Puliaion Hous hp://www.irphous.om Rliailiy Analysis of a Bridg and Paralll Sris Nworks wih

More information

Control Systems. Modelling Physical Systems. Assoc.Prof. Haluk Görgün. Gears DC Motors. Lecture #5. Control Systems. 10 March 2013

Control Systems. Modelling Physical Systems. Assoc.Prof. Haluk Görgün. Gears DC Motors. Lecture #5. Control Systems. 10 March 2013 Lcur #5 Conrol Sy Modlling Phyicl Sy Gr DC Moor Aoc.Prof. Hluk Görgün 0 Mrch 03 Conrol Sy Aoc. Prof. Hluk Görgün rnfr Funcion for Sy wih Gr Gr provid chnicl dvng o roionl y. Anyon who h riddn 0-pd bicycl

More information

ELECTRIC VELOCITY SERVO REGULATION

ELECTRIC VELOCITY SERVO REGULATION ELECIC VELOCIY SEVO EGULAION Gorg W. Younkin, P.E. Lif FELLOW IEEE Indusril Conrols Consuling, Di. Bulls Ey Mrking, Inc. Fond du Lc, Wisconsin h prformnc of n lcricl lociy sro is msur of how wll h sro

More information

The Procedure Abstraction Part II: Symbol Tables and Activation Records

The Procedure Abstraction Part II: Symbol Tables and Activation Records Th Produr Absrion Pr II: Symbol Tbls nd Aivion Rords Th Produr s Nm Sp Why inrodu lxil soping? Provids ompil-im mhnism for binding vribls Ls h progrmmr inrodu lol nms How n h ompilr kp rk of ll hos nms?

More information

Special Curves of 4D Galilean Space

Special Curves of 4D Galilean Space Irol Jourl of Mhml Egrg d S ISSN : 77-698 Volum Issu Mrh hp://www.jms.om/ hps://ss.googl.om/s/jmsjourl/ Spl Curvs of D ll Sp Mhm Bkş Mhmu Ergü Alpr Osm Öğrmş Fır Uvrsy Fuly of S Dprm of Mhms 9 Elzığ Türky

More information

Fourier Series and Parseval s Relation Çağatay Candan Dec. 22, 2013

Fourier Series and Parseval s Relation Çağatay Candan Dec. 22, 2013 Fourir Sris nd Prsvl s Rlion Çğy Cndn Dc., 3 W sudy h m problm EE 3 M, Fll3- in som dil o illusr som conncions bwn Fourir sris, Prsvl s rlion nd RMS vlus. Q. ps h signl sin is h inpu o hlf-wv rcifir circui

More information

Pupil / Class Record We can assume a word has been learned when it has been either tested or used correctly at least three times.

Pupil / Class Record We can assume a word has been learned when it has been either tested or used correctly at least three times. 2 Pupi / Css Rr W ssum wr hs b r wh i hs b ihr s r us rry s hr ims. Nm: D Bu: fr i bus brhr u firs hf hp hm s uh i iv iv my my mr muh m w ih w Tik r pp push pu sh shu sisr s sm h h hir hr hs im k w vry

More information

International Journal on Recent and Innovation Trends in Computing and Communication ISSN: Volume: 5 Issue:

International Journal on Recent and Innovation Trends in Computing and Communication ISSN: Volume: 5 Issue: Inrnionl Journl on Rn nd Innovion rnds in Compuing nd Communiion ISSN: -869 Volum: Issu: 78 97 Dvlopmn of n EPQ Modl for Drioring Produ wih Sok nd Dmnd Dpndn Produion r undr Vril Crrying Cos nd Pril Bklogging

More information

EE Control Systems LECTURE 11

EE Control Systems LECTURE 11 Up: Moy, Ocor 5, 7 EE 434 - Corol Sy LECTUE Copyrigh FL Lwi 999 All righ rrv POLE PLACEMET A STEA-STATE EO Uig fc, o c ov h clo-loop pol o h h y prforc iprov O c lo lc uil copor o oi goo y- rcig y uyig

More information

Incremental DFT Based Search Algorithm for Similar Sequence

Incremental DFT Based Search Algorithm for Similar Sequence Inrnl DFT Bsd Srh Algorih or Siilr Squn Qun hng, hiki Fng, nd Ming hu Dprn o Auoion, Univrsiy o Sin nd Thnology o Chin, Hi, 37, P.R. Chin qzhng@us.du.n nzhiki@il.us.du.n Absr. This ppr bgins wih nw lgorih

More information

Equations and Boundary Value Problems

Equations and Boundary Value Problems Elmn Diffnil Equions nd Bound Vlu Poblms Bo. & DiPim, 9 h Ediion Chp : Sond Od Diffnil Equions 6 คณ ตศาสตร ว ศวกรรม สาขาว ชาว ศวกรรมคอมพ วเตอร ป การศ กษา /555 ผศ.ดร.อร ญญา ผศ.ดร.สมศ กด วล ยร ชต Topis Homognous

More information

Transfer function and the Laplace transformation

Transfer function and the Laplace transformation Lab No PH-35 Porland Sa Univriy A. La Roa Tranfr funcion and h Laplac ranformaion. INTRODUTION. THE LAPLAE TRANSFORMATION L 3. TRANSFER FUNTIONS 4. ELETRIAL SYSTEMS Analyi of h hr baic paiv lmn R, and

More information

Relation between Fourier Series and Transform

Relation between Fourier Series and Transform EE 37-3 8 Ch. II: Inro. o Sinls Lcur 5 Dr. Wih Abu-Al-Su Rlion bwn ourir Sris n Trnsform Th ourir Trnsform T is riv from h finiion of h ourir Sris S. Consir, for xmpl, h prioic complx sinl To wih prio

More information

INF5820 MT 26 OCT 2012

INF5820 MT 26 OCT 2012 INF582 MT 26 OCT 22 H22 Jn Tor Lønnng l@.uo.no Tody Ssl hn rnslon: Th nosy hnnl odl Word-bsd IBM odl Trnng SMT xpl En o lgd n r d bygg..9 h.6 d.3.9 rgh.9 wh.4 buldng.45 oo.3 rd.25 srgh.7 by.3 onsruon.33

More information

A Review of Dynamic Models Used in Simulation of Gear Transmissions

A Review of Dynamic Models Used in Simulation of Gear Transmissions ANALELE UNIVERSITĂłII ETIMIE MURGU REŞIłA ANUL XXI NR. ISSN 5-797 Zol-Ios Ko Io-ol Mulu A Rvw o ls Us Sulo o G Tsssos Th vsgo o lv s lu gg g olg l us o sov sg u o pps g svl s oug o h ps. Th pupos o h ols

More information

Jonathan Turner Exam 2-10/28/03

Jonathan Turner Exam 2-10/28/03 CS Algorihm n Progrm Prolm Exm Soluion S Soluion Jonhn Turnr Exm //. ( poin) In h Fioni hp ruur, u wn vrx u n i prn v u ing u v i v h lry lo hil in i l m hil o om ohr vrx. Suppo w hng hi, o h ing u i prorm

More information

HIGHER ORDER DIFFERENTIAL EQUATIONS

HIGHER ORDER DIFFERENTIAL EQUATIONS Prof Enriqu Mtus Nivs PhD in Mthmtis Edution IGER ORDER DIFFERENTIAL EQUATIONS omognous linr qutions with onstnt offiints of ordr two highr Appl rdution mthod to dtrmin solution of th nonhomognous qution

More information

More on FT. Lecture 10 4CT.5 3CT.3-5,7,8. BME 333 Biomedical Signals and Systems - J.Schesser

More on FT. Lecture 10 4CT.5 3CT.3-5,7,8. BME 333 Biomedical Signals and Systems - J.Schesser Mr n FT Lcur 4CT.5 3CT.3-5,7,8 BME 333 Bimdicl Signls nd Sysms - J.Schssr 43 Highr Ordr Diffrniin d y d x, m b Y b X N n M m N M n n n m m n m n d m d n m Y n d f n [ n ] F d M m bm m X N n n n n n m p

More information

Derivation of the differential equation of motion

Derivation of the differential equation of motion Divion of h iffnil quion of oion Fis h noions fin h will us fo h ivion of h iffnil quion of oion. Rollo is hough o -insionl isk. xnl ius of h ll isnc cn of ll (O) - IDU s cn of gviy (M) θ ngl of inclinion

More information

Engine Thrust. From momentum conservation

Engine Thrust. From momentum conservation Airbrhing Propulsion -1 Airbrhing School o Arospc Enginring Propulsion Ovrviw w will b xmining numbr o irbrhing propulsion sysms rmjs, urbojs, urbons, urboprops Prormnc prmrs o compr hm, usul o din som

More information

T h e C S E T I P r o j e c t

T h e C S E T I P r o j e c t T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T

More information

Chapter 5 Transient Analysis

Chapter 5 Transient Analysis hpr 5 rs Alyss Jsug Jg ompl rspos rs rspos y-s rspos m os rs orr co orr Dffrl Equo. rs Alyss h ffrc of lyss of crcus wh rgy sorg lms (ucors or cpcors) & m-ryg sgls wh rss crcus s h h quos rsulg from r

More information

Physics 160 Lecture 3. R. Johnson April 6, 2015

Physics 160 Lecture 3. R. Johnson April 6, 2015 Physics 6 Lcur 3 R. Johnson April 6, 5 RC Circui (Low-Pass Filr This is h sam RC circui w lookd a arlir h im doma, bu hr w ar rsd h frquncy rspons. So w pu a s wav sad of a sp funcion. whr R C RC Complx

More information

Study on Non-linear Responses of Eccentric Structure

Study on Non-linear Responses of Eccentric Structure Th 4 h World ofr o Erh Egrg or -7 8 Bg h Sd o No-lr Rpo of Er Srr Hdz WATANABE oh USUNI Ar TASAI 3 Grd Sd Dpr of Arhr ooh Nol Uvr ooh Jp Ao Profor Dpr of Arhr ooh Nol Uvr ooh Jp ABSTRAT : 3 Profor Dpr

More information

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline.

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline. Dlin Curvs Dlin Curvs ha lo flow ra vs. im ar h mos ommon ools for forasing roduion and monioring wll rforman in h fild. Ths urvs uikly show by grahi mans whih wlls or filds ar roduing as xd or undr roduing.

More information

1 Finite Automata and Regular Expressions

1 Finite Automata and Regular Expressions 1 Fini Auom nd Rgulr Exprion Moivion: Givn prn (rgulr xprion) for ring rching, w migh wn o convr i ino drminiic fini uomon or nondrminiic fini uomon o mk ring rching mor fficin; drminiic uomon only h o

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

Appendix. In the absence of default risk, the benefit of the tax shield due to debt financing by the firm is 1 C E C

Appendix. In the absence of default risk, the benefit of the tax shield due to debt financing by the firm is 1 C E C nx. Dvon o h n wh In h sn o ul sk h n o h x shl u o nnng y h m s s h ol ouon s h num o ssus s h oo nom x s h sonl nom x n s h v x on quy whh s wgh vg o vn n l gns x s. In hs s h o sonl nom xs on h x shl

More information

Quantum Harmonic Oscillator

Quantum Harmonic Oscillator Quu roc Oscllor Quu roc Oscllor 6 Quu Mccs Prof. Y. F. C Quu roc Oscllor Quu roc Oscllor D S..O.:lr rsorg forc F k, k s forc cos & prbolc pol. V k A prcl oscllg roc pol roc pol s u po of sbly sys 6 Quu

More information

2. Transfer function. Kanazawa University Microelectronics Research Lab. Akio Kitagawa

2. Transfer function. Kanazawa University Microelectronics Research Lab. Akio Kitagawa . ransfr funion Kanazawa Univrsiy Mirolronis Rsarh Lab. Akio Kiagawa . Wavforms in mix-signal iruis Configuraion of mix-signal sysm x Digial o Analog Analog o Digial Anialiasing Digial moohing Filr Prossor

More information

The Mathematics of Harmonic Oscillators

The Mathematics of Harmonic Oscillators Th Mhcs of Hronc Oscllors Spl Hronc Moon In h cs of on-nsonl spl hronc oon (SHM nvolvng sprng wh sprng consn n wh no frcon, you rv h quon of oon usng Nwon's scon lw: con wh gvs: 0 Ths s sos wrn usng h

More information

Let's revisit conditional probability, where the event M is expressed in terms of the random variable. P Ax x x = =

Let's revisit conditional probability, where the event M is expressed in terms of the random variable. P Ax x x = = L's rvs codol rol whr h v M s rssd rs o h rdo vrl. L { M } rrr v such h { M } Assu. { } { A M} { A { } } M < { } { } A u { } { } { A} { A} ( A) ( A) { A} A A { A } hs llows us o cosdr h cs wh M { } [ (

More information

Department of Electronics & Telecommunication Engineering C.V.Raman College of Engineering

Department of Electronics & Telecommunication Engineering C.V.Raman College of Engineering Lcur No Lcur-6-9 Ar rdig his lsso, you will lr ou Fourir sris xpsio rigoomric d xpoil Propris o Fourir Sris Rspos o lir sysm Normlizd powr i Fourir xpsio Powr spcrl dsiy Ec o rsr ucio o PSD. FOURIER SERIES

More information

Lecture 4: Laplace Transforms

Lecture 4: Laplace Transforms Lur 4: Lapla Transforms Lapla and rlad ransformaions an b usd o solv diffrnial quaion and o rdu priodi nois in signals and imags. Basially, hy onvr h drivaiv opraions ino mulipliaion, diffrnial quaions

More information

Lecture 2: Current in RC circuit D.K.Pandey

Lecture 2: Current in RC circuit D.K.Pandey Lcur 2: urrn in circui harging of apacior hrough Rsisr L us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R and a ky K in sris. Whn h ky K is swichd on, h charging

More information

Handout on. Crystal Symmetries and Energy Bands

Handout on. Crystal Symmetries and Energy Bands dou o Csl s d g Bds I hs lu ou wll l: Th loshp bw ss d g bds h bs of sp-ob ouplg Th loshp bw ss d g bds h ps of sp-ob ouplg C 7 pg 9 Fh Coll Uvs d g Bds gll hs oh Th sl pol ss ddo o h l slo s: Fo pl h

More information

Erlkönig. t t.! t t. t t t tj "tt. tj t tj ttt!t t. e t Jt e t t t e t Jt

Erlkönig. t t.! t t. t t t tj tt. tj t tj ttt!t t. e t Jt e t t t e t Jt Gsng Po 1 Agio " " lkö (Compl by Rhol Bckr, s Moifi by Mrk S. Zimmr)!! J "! J # " c c " Luwig vn Bhovn WoO 131 (177) I Wr Who!! " J J! 5 ri ris hro' h spä h, I urch J J Nch rk un W Es n wil A J J is f

More information

Advanced Queueing Theory. M/G/1 Queueing Systems

Advanced Queueing Theory. M/G/1 Queueing Systems Advand Quung Thory Ths slds ar rad by Dr. Yh Huang of Gorg Mason Unvrsy. Sudns rgsrd n Dr. Huang's ourss a GMU an ma a sngl mahn-radabl opy and prn a sngl opy of ah sld for hr own rfrn, so long as ah sld

More information

DETERMINATION OF THERMAL STRESSES OF A THREE DIMENSIONAL TRANSIENT THERMOELASTIC PROBLEM OF A SQUARE PLATE

DETERMINATION OF THERMAL STRESSES OF A THREE DIMENSIONAL TRANSIENT THERMOELASTIC PROBLEM OF A SQUARE PLATE DRMINAION OF HRMAL SRSSS OF A HR DIMNSIONAL RANSIN HRMOLASIC PROBLM OF A SQUAR PLA Wrs K. D Dpr o Mics Sr Sivji Co Rjr Mrsr Idi *Aor or Corrspodc ABSRAC prs ppr ds wi driio o prr disribio ow prr poi o

More information

Ash Wednesday. First Introit thing. * Dómi- nos. di- di- nos, tú- ré- spi- Ps. ne. Dó- mi- Sál- vum. intra-vé-runt. Gló- ri-

Ash Wednesday. First Introit thing. * Dómi- nos. di- di- nos, tú- ré- spi- Ps. ne. Dó- mi- Sál- vum. intra-vé-runt. Gló- ri- sh Wdsdy 7 gn mult- tú- st Frst Intrt thng X-áud m. ns ní- m-sr-cór- Ps. -qu Ptr - m- Sál- vum m * usqu 1 d fc á-rum sp- m-sr-t- ó- num Gló- r- Fí- l- Sp-rí- : quó-n- m ntr-vé-runt á- n-mm c * m- quó-n-

More information

Chapter 3. The Fourier Series

Chapter 3. The Fourier Series Chpr 3 h Fourir Sris Signls in h im nd Frquny Domin INC Signls nd Sysms Chpr 3 h Fourir Sris Eponnil Funion r j ros jsin ) INC Signls nd Sysms Chpr 3 h Fourir Sris Odd nd Evn Evn funion : Odd funion :

More information

Adrian Sfarti University of California, 387 Soda Hall, UC Berkeley, California, USA

Adrian Sfarti University of California, 387 Soda Hall, UC Berkeley, California, USA Innionl Jonl of Phoonis n Oil Thnolo Vol. 3 Iss. : 36-4 Jn 7 Rliisi Dnis n lonis in Unifol l n in Unifol Roin s-th Gnl ssions fo h loni 4-Vo Ponil in Sfi Unisi of Clifoni 387 So Hll UC Bkl Clifoni US s@ll.n

More information

EEE 303: Signals and Linear Systems

EEE 303: Signals and Linear Systems 33: Sigls d Lir Sysms Orhogoliy bw wo sigls L us pproim fucio f () by fucio () ovr irvl : f ( ) = c( ); h rror i pproimio is, () = f() c () h rgy of rror sigl ovr h irvl [, ] is, { }{ } = f () c () d =

More information

Chapter 4 Circular and Curvilinear Motions

Chapter 4 Circular and Curvilinear Motions Chp 4 Cicul n Cuilin Moions H w consi picls moing no long sigh lin h cuilin moion. W fis su h cicul moion, spcil cs of cuilin moion. Anoh mpl w h l sui li is h pojcil..1 Cicul Moion Unifom Cicul Moion

More information

Lecture 6 Thermionic Engines

Lecture 6 Thermionic Engines Ltur 6 hrmioni ngins Rviw Rihrdson formul hrmioni ngins Shotty brrir nd diod pn juntion nd diod disussion.997 Copyright Gng Chn, MI For.997 Dirt Solr/hrml to ltril nrgy Convrsion WARR M. ROHSOW HA AD MASS

More information

Integral Calculus What is integral calculus?

Integral Calculus What is integral calculus? Intgral Calulus What is intgral alulus? In diffrntial alulus w diffrntiat a funtion to obtain anothr funtion alld drivativ. Intgral alulus is onrnd with th opposit pross. Rvrsing th pross of diffrntiation

More information

2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control.

2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control. 211 8 Il C Ell E Cpu S Au Cl Aly Cll I Al G Cl-Lp I Appl Pu DC S k u PD l R 1 F O 1 1 U Plé V Só ó A Nu Tlí S/N Pqu Cí y Tló TECNOTA K C V-S l E-l: @upux 87@l A Uully l ppl y l py ly x l l H l- lp uu u

More information

Air Filter 90-AF30 to 90-AF60

Air Filter 90-AF30 to 90-AF60 Ai il -A o -A6 Ho o Od A /Smi-sndd: Sl on h fo o. /Smi-sndd symol: Whn mo hn on spifiion is uid, indi in lphnumi od. Exmpl) -A-- Sis ompil ih sondy is Mil siion Smi-sndd Thd yp Po siz Mouning lo diion

More information

P441 Analytical Mechanics - I. Coupled Oscillators. c Alex R. Dzierba

P441 Analytical Mechanics - I. Coupled Oscillators. c Alex R. Dzierba Lecure 3 Mondy - Deceber 5, 005 Wrien or ls upded: Deceber 3, 005 P44 Anlyicl Mechnics - I oupled Oscillors c Alex R. Dzierb oupled oscillors - rix echnique In Figure we show n exple of wo coupled oscillors,

More information

Control System Engineering (EE301T) Assignment: 2

Control System Engineering (EE301T) Assignment: 2 Conrol Sysm Enginring (EE0T) Assignmn: PART-A (Tim Domain Analysis: Transin Rspons Analysis). Oain h rspons of a uniy fdack sysm whos opn-loop ransfr funcion is (s) s ( s 4) for a uni sp inpu and also

More information

Get Funky this Christmas Season with the Crew from Chunky Custard

Get Funky this Christmas Season with the Crew from Chunky Custard Hol Gd Chcllo Adld o Hdly Fdy d Sudy Nhs Novb Dcb 2010 7p 11.30p G Fuky hs Chss Sso wh h Cw fo Chuky Cusd Fdy Nhs $99pp Sudy Nhs $115pp Tck pc cluds: Full Chss d buff, 4.5 hou bv pck, o sop. Ts & Codos

More information

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

A Simple Code Generator. Code generation Algorithm. Register and Address Descriptors. Example 3/31/2008. Code Generation

A Simple Code Generator. Code generation Algorithm. Register and Address Descriptors. Example 3/31/2008. Code Generation A Simpl Co Gnrtor Co Gnrtion Chptr 8 II Gnrt o for singl si lok How to us rgistrs? In most mhin rhitturs, som or ll of th oprnsmust in rgistrs Rgistrs mk goo tmporris Hol vlus tht r omput in on si lok

More information

Inverse Fourier Transform. Properties of Continuous time Fourier Transform. Review. Linearity. Reading Assignment Oppenheim Sec pp.289.

Inverse Fourier Transform. Properties of Continuous time Fourier Transform. Review. Linearity. Reading Assignment Oppenheim Sec pp.289. Convrgnc of ourir Trnsform Rding Assignmn Oppnhim Sc 42 pp289 Propris of Coninuous im ourir Trnsform Rviw Rviw or coninuous-im priodic signl x, j x j d Invrs ourir Trnsform 2 j j x d ourir Trnsform Linriy

More information

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o

More information

Contraction Mapping Principle Approach to Differential Equations

Contraction Mapping Principle Approach to Differential Equations epl Journl of Science echnology 0 (009) 49-53 Conrcion pping Principle pproch o Differenil Equions Bishnu P. Dhungn Deprmen of hemics, hendr Rn Cmpus ribhuvn Universiy, Khmu epl bsrc Using n eension of

More information

Chapter 1 Basic Concepts

Chapter 1 Basic Concepts Ch Bsc Cocs oduco od: X X ε ε ε ε ε O h h foog ssuos o css ε ε ε ε ε N Co No h X Chcscs of od: cos c ddc (ucod) d s of h soss dd of h ssocd c S qusos sd: Wh f h cs of h soss o cos d dd o h ssocd s? Wh

More information

Wave Phenomena Physics 15c

Wave Phenomena Physics 15c Wv hnon hyscs 5c cur 4 Coupl Oscllors! H& con 4. Wh W D s T " u forc oscllon " olv h quon of oon wh frcon n foun h sy-s soluon " Oscllon bcos lr nr h rsonnc frquncy " hs chns fro 0 π/ π s h frquncy ncrss

More information

CSE 245: Computer Aided Circuit Simulation and Verification

CSE 245: Computer Aided Circuit Simulation and Verification CSE 45: Compur Aidd Circui Simulaion and Vrificaion Fall 4, Sp 8 Lcur : Dynamic Linar Sysm Oulin Tim Domain Analysis Sa Equaions RLC Nwork Analysis by Taylor Expansion Impuls Rspons in im domain Frquncy

More information

Library Support. Netlist Conditioning. Observe Point Assessment. Vector Generation/Simulation. Vector Compression. Vector Writing

Library Support. Netlist Conditioning. Observe Point Assessment. Vector Generation/Simulation. Vector Compression. Vector Writing hpr 2 uomi T Prn Gnrion Fundmnl hpr 2 uomi T Prn Gnrion Fundmnl Lirry uppor Nli ondiioning Orv Poin mn Vor Gnrion/imulion Vor omprion Vor Wriing Figur 2- Th Ovrll Prn Gnrion Pro Dign-or-T or Digil I nd

More information

Three Dimensional Coordinate Geometry

Three Dimensional Coordinate Geometry HKCWCC dvned evel Pure Mhs. / -D Co-Geomer Three Dimensionl Coordine Geomer. Coordine of Poin in Spe Z XOX, YOY nd ZOZ re he oordine-es. P,, is poin on he oordine plne nd is lled ordered riple. P,, X Y

More information

NHPP and S-Shaped Models for Testing the Software Failure Process

NHPP and S-Shaped Models for Testing the Software Failure Process Irol Jourl of Ls Trds Copug (E-ISSN: 45-5364 8 Volu, Issu, Dcr NHPP d S-Shpd Modls for Tsg h Sofwr Flur Procss Dr. Kr Arr Asss Profssor K.J. Soy Isu of Mg Suds & Rsrch Vdy Ngr Vdy Vhr Mu. Id. dshuh_3@yhoo.co/rrr@ssr.soy.du

More information

12 - M G P L Z - M9BW. Port type. Bore size ø12, ø16 20/25/32/40/50/ MPa 10 C to 60 C (With no condensation) 50 to 400 mm/s +1.

12 - M G P L Z - M9BW. Port type. Bore size ø12, ø16 20/25/32/40/50/ MPa 10 C to 60 C (With no condensation) 50 to 400 mm/s +1. ris - MP - Compt gui ylinr ø, ø, ø, ø, ø, ø, ø, ø ow to Orr Cln sris lif typ (with spilly trt sliing prts) Vuum sution typ (with spilly trt sliing prts) ir ylinr otry tutor - M P - - MW ll ushing ring

More information

Inventory Model with Quadratic Demand under the Two Warehouse Management System

Inventory Model with Quadratic Demand under the Two Warehouse Management System Prin : - nlin : - A K Mlik l. / nrnionl Jornl of Enginring nd hnology JE nnory Modl wih Qdri Dmnd ndr h wo Wrhos Mngmn ysm A K Mlik Dipk Chkrory Kpil Kmr Bnsl nd * ish Kmr Assoi Profssor Dprmn of Mhmis

More information

SAN JOSE CITY COLLEGE PHYSICAL EDUCATION BUILDING AND RENOVATED LAB BUILDING SYMBOL LIST & GENERAL NOTES - MECHANICAL

SAN JOSE CITY COLLEGE PHYSICAL EDUCATION BUILDING AND RENOVATED LAB BUILDING SYMBOL LIST & GENERAL NOTES - MECHANICAL S SRUUR OR OORO SU sketch SYO SRPO OO OU O SUPPOR YP SUPPOR O UR SOS OVR SOS (xwx) X W (S) RR RWS U- R R OR ROO OR P S SPR SO S OS OW "Wx00"x0" 000.0, 8/7.0 Z U- R R UPPR ROO S S S SPR SO S OS OW 0"Wx0"x90"

More information

CS 541 Algorithms and Programs. Exam 2 Solutions. Jonathan Turner 11/8/01

CS 541 Algorithms and Programs. Exam 2 Solutions. Jonathan Turner 11/8/01 CS 1 Algorim nd Progrm Exm Soluion Jonn Turnr 11/8/01 B n nd oni, u ompl. 1. (10 poin). Conidr vrion of or p prolm wi mulipliiv o. In i form of prolm, lng of p i produ of dg lng, rr n um. Explin ow or

More information

Consider a system of 2 simultaneous first order linear equations

Consider a system of 2 simultaneous first order linear equations Soluon of sysms of frs ordr lnar quaons onsdr a sysm of smulanous frs ordr lnar quaons a b c d I has h alrna mar-vcor rprsnaon a b c d Or, n shorhand A, f A s alrady known from con W know ha h abov sysm

More information

SYMMETRICAL COMPONENTS

SYMMETRICAL COMPONENTS SYMMETRCA COMPONENTS Syl oponn llow ph un of volg n un o pl y h p ln yl oponn Con h ph ln oponn wh Engy Convon o 4 o o wh o, 4 o, 6 o Engy Convon SYMMETRCA COMPONENTS Dfn h opo wh o Th o of pho : pov ph

More information

EXERCISE - 01 CHECK YOUR GRASP

EXERCISE - 01 CHECK YOUR GRASP DEFNTE NTEGRATON EXERCSE - CHECK YOUR GRASP. ( ) d [ ] d [ ] d d ƒ( ) ƒ '( ) [ ] [ ] 8 5. ( cos )( c)d 8 ( cos )( c)d + 8 ( cos )( c) d 8 ( cos )( c) d sic + cos 8 is lwys posiiv f() d ( > ) ms f() is

More information

FL/VAL ~RA1::1. Professor INTERVI of. Professor It Fr recru. sor Social,, first of all, was. Sys SDC? Yes, as a. was a. assumee.

FL/VAL ~RA1::1. Professor INTERVI of. Professor It Fr recru. sor Social,, first of all, was. Sys SDC? Yes, as a. was a. assumee. B Pror NTERV FL/VAL ~RA1::1 1 21,, 1989 i n or Socil,, fir ll, Pror Fr rcru Sy Ar you lir SDC? Y, om um SM: corr n 'd m vry ummr yr. Now, y n y, f pr my ry for ummr my 1 yr Un So vr ummr cour d rr o l

More information

Data Structures Lecture 3

Data Structures Lecture 3 Rviw: Rdix sor vo Rdix::SorMgr(isr& i, osr& o) 1. Dclr lis L 2. Rd h ifirs i sr i io lis L. Us br fucio TilIsr o pu h ifirs i h lis. 3. Dclr igr p. Vribl p is h chrcr posiio h is usd o slc h buck whr ifir

More information

A Comparative Study of PID and Fuzzy Controller for Speed Control of Brushless DC Motor Drive

A Comparative Study of PID and Fuzzy Controller for Speed Control of Brushless DC Motor Drive Inrnonl srh ournl o Engnrng n hnology IE -ISSN: 95-56 olu: Issu: -16 www.rj.n p-issn: 95-7 A Coprv Suy o PID n uzzy Conrollr or Sp Conrol o Brushlss DC Moor Drv 1 Prrn r horg, gsh houhr 1PG Sun, Elrl Engnrng

More information

UNSTEADY HEAT TRANSFER

UNSTEADY HEAT TRANSFER UNSADY HA RANSFR Mny h rnsfr problms rquir h undrsnding of h ompl im hisory of h mprur vriion. For mpl, in mllurgy, h h ring pross n b onrolld o dirly ff h hrrisis of h prossd mrils. Annling (slo ool)

More information

Charging of capacitor through inductor and resistor

Charging of capacitor through inductor and resistor cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.

More information

The model proposed by Vasicek in 1977 is a yield-based one-factor equilibrium model given by the dynamic

The model proposed by Vasicek in 1977 is a yield-based one-factor equilibrium model given by the dynamic h Vsick modl h modl roosd by Vsick in 977 is yild-bsd on-fcor quilibrium modl givn by h dynmic dr = b r d + dw his modl ssums h h shor r is norml nd hs so-clld "mn rvring rocss" (undr Q. If w u r = b/,

More information

1 Introduction to Modulo 7 Arithmetic

1 Introduction to Modulo 7 Arithmetic 1 Introution to Moulo 7 Arithmti Bor w try our hn t solvin som hr Moulr KnKns, lt s tk los look t on moulr rithmti, mo 7 rithmti. You ll s in this sminr tht rithmti moulo prim is quit irnt rom th ons w

More information

Aquauno Video 6 Plus Page 1

Aquauno Video 6 Plus Page 1 Connt th timr to th tp. Aquuno Vio 6 Plus Pg 1 Usr mnul 3 lik! For Aquuno Vio 6 (p/n): 8456 For Aquuno Vio 6 Plus (p/n): 8413 Opn th timr unit y prssing th two uttons on th sis, n fit 9V lklin ttry. Whn

More information

Chapter 7. Now, for 2) 1. 1, if z = 1, Thus, Eq. (7.20) holds

Chapter 7. Now, for 2) 1. 1, if z = 1, Thus, Eq. (7.20) holds Chapr 7, n, 7 Ipuls rspons of h ovng avrag flr s: h[, ohrws sn / / Is frquny rspons s: sn / Now, for a BR ransfr funon,, For h ovng-avrag flr, sn / W shall show by nduon ha sn / sn / sn /,, Now, for sn

More information

PHYSICS 1210 Exam 1 University of Wyoming 14 February points

PHYSICS 1210 Exam 1 University of Wyoming 14 February points PHYSICS 1210 Em 1 Uniersiy of Wyoming 14 Februry 2013 150 poins This es is open-noe nd closed-book. Clculors re permied bu compuers re no. No collborion, consulion, or communicion wih oher people (oher

More information

Suggested Solution for Pure Mathematics 2011 By Y.K. Ng (last update: 8/4/2011) Paper I. (b) (c)

Suggested Solution for Pure Mathematics 2011 By Y.K. Ng (last update: 8/4/2011) Paper I. (b) (c) per I. Le α 7 d β 7. The α d β re he roos o he equio, such h α α, β β, --- α β d αβ. For, α β For, α β α β αβ 66 The seme is rue or,. ssume Cosider, α β d α β y deiiio α α α α β or some posiive ieer.

More information

Institute of Actuaries of India

Institute of Actuaries of India Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6

More information

EXERCISE - 01 CHECK YOUR GRASP

EXERCISE - 01 CHECK YOUR GRASP DIFFERENTIAL EQUATION EXERCISE - CHECK YOUR GRASP 7. m hn D() m m, D () m m. hn givn D () m m D D D + m m m m m m + m m m m + ( m ) (m ) (m ) (m + ) m,, Hnc numbr of valus of mn will b. n ( ) + c sinc

More information

Fourier. Continuous time. Review. with period T, x t. Inverse Fourier F Transform. x t. Transform. j t

Fourier. Continuous time. Review. with period T, x t. Inverse Fourier F Transform. x t. Transform. j t Coninuous im ourir rnsform Rviw. or coninuous-im priodic signl x h ourir sris rprsnion is x x j, j 2 d wih priod, ourir rnsform Wh bou priodic signls? W willl considr n priodic signl s priodic signl wih

More information

( ) C R. υ in RC 1. cos. ,sin. ω ω υ + +

( ) C R. υ in RC 1. cos. ,sin. ω ω υ + + Oscillaors. Thory of Oscillaions. Th lad circui, h lag circui and h lad-lag circui. Th Win Bridg oscillaor. Ohr usful oscillaors. Th 555 Timr. Basic Dscripion. Th S flip flop. Monosabl opraion of h 555

More information

Boyce/DiPrima 9 th ed, Ch 7.8: Repeated Eigenvalues

Boyce/DiPrima 9 th ed, Ch 7.8: Repeated Eigenvalues Boy/DiPrima 9 h d Ch 7.8: Rpad Eignvalus Elmnary Diffrnial Equaions and Boundary Valu Problms 9 h diion by William E. Boy and Rihard C. DiPrima 9 by John Wily & Sons In. W onsidr again a homognous sysm

More information

t=0 t>0: + vr - i dvc Continuation

t=0 t>0: + vr - i dvc Continuation hapr Ga Dlay and rcus onnuaon s rcu Equaon >: S S Ths dffrnal quaon, oghr wh h nal condon, fully spcfs bhaor of crcu afr swch closs Our n challng: larn how o sol such quaons TUE/EE 57 nwrk analys 4/5 NdM

More information

Section 2: The Z-Transform

Section 2: The Z-Transform Scion : h -rnsform Digil Conrol Scion : h -rnsform In linr discr-im conrol sysm linr diffrnc quion chrcriss h dynmics of h sysm. In ordr o drmin h sysm s rspons o givn inpu, such diffrnc quion mus b solvd.

More information