Introduction. Voice Coil Motors. Introduction - Voice Coil Velocimeter Electromechanical Systems. F = Bli

Size: px
Start display at page:

Download "Introduction. Voice Coil Motors. Introduction - Voice Coil Velocimeter Electromechanical Systems. F = Bli"

Transcription

1 UNIVERSITY O TECHNOLOGY, SYDNEY ACULTY O ENGINEERING 4853 Elecroechncl Syses Voce Col Moors Topcs o cover:.. Mnec Crcus 3. EM n Voce Col 4. orce n Torque 5. Mhecl Moel 6. Perornce Voce cols re wely use lou spekers. When ece by n elecrcl curren o spece wveor, he voce col crryn he curren wll ove (vbre) n prouce soun by he spece wveor snce he orce l s proporonl o he curren. Ths e cn be eene o rec rve lner cuors or pplcons h requre posonn over sll rne ro crons o nchs, such s be seern rrors, plo vlve conrol, n hr sk rves. Core Voce Col - Voce Col Veloceer - Voce Col Veloceer In he vbron es o echncl enneern, sple elecronec evce conssn o wre wrppe col n ne s use o boh rve he syse (voce col oor) n esure he velocy o he syse (veloceer). Enlre vew o he voce col veloceer

2 - Hr Dsk Drve Hr sk rve or rec ccess sore evces s one o he jor pplcons or voce col oors. - Hr Dsk Drve (Con.) Schec cu wy vew o hr sk - Hr Dsk Drve (Con.) - Hr Dsk Drve (Con.) rushless spnle oor n he rve crcu bor. Ol hr sk rves use seppn oor or poson conrol o re/wre he

3 - Hr Dsk Drve (Con.) - Hr Dsk Drve (Con.) New hr sk rves use voce col oors or poson conrol o re/wre he Schec llusron o re/wre he poson conrol usn voce col oors or lre hr sks - Hr Dsk Drve (Con.) - Hr Dsk Drve (Con.) Re/wre he o sll sze hr sk Re/wre he o sll sze hr sk

4 - Generl Purpose Voce Col Lner Acuor Mnec Crcus - Lerl Voce Col Moors The e o voce col oor/cuor cn be eploye or enerl purpose lner rves. Movn Col Movn Col Movn Col Movn Col The srucure cn be eher cylnrcl or recnulr Mnec Crcus - Rory Voce Col Moors EM n Voce Col - Arc Type Rory Voce Col Moor l l Re/Wre He Movn Col Movn Col Cross secons o rory voce col oors use n hr sk rves The e n he voce col cn be clcule by he ry s lw e λ λ λ + λ, λ L, n λ re he lu lnkes o he voce col ue o he curren n he col n he pernen ne. Thereore, e L λ + Noe h L s nepenen o col poson. R

5 l Φ EM n Voce Col - Arc Type Rory Voce Col Moor I he col hs N urns, he sel nucnce s nepenen o he col poson n cn be eerne s N L R core R core s he relucnce o he core. l The nuce e n he col ue o he pernen nes cn be clcule s λ e N l v v v / s he spee n he lu ensy n r p. orce n Torque - Arc Type Rory Voce Col Moor The ol orce cn on he col cn be clcule by N l Assue he snce beween he col cener n he sh s R. The orque prouce by he col s hen T R N l R Noe h he orce cn lso be clcule by W ' L L + I + I L Snce L / n L /, we hve he bove resuls. Mhecl Moel - Elecrcl Crcu Equon The elecrcl crcu equon or he voce col s V ( L) λ R + + R L or he rc ype rory voce col oor, he sel nucnce s nepen-en o he col poson, n he bove equon becoes V e V R + L + e e λ / N l v v s he nuce e n he col ue o he pernen ne, N l s he e consn, n v / s he spee. Mhecl Moel - Mechncl Equons The echncl syse or hr sk rve s llusre on he rh hn se. y Newon s lw, we hve v lo lo + v Col o ss s he lo orce ue o he sprn n per. Sprn Dper s he elecronec orce prouce by he curren n he col, N l he elecronec orce consn, n

6 Mhecl Moel - Se Equons When he elecrcl n echncl equons epresse n he or o se equons, we obn R L L v + L V v v n v These equons cn be solve oeher wh nl conons ( ), v( ) v, n ( ) Perornce - Wh Curren Source Supply Wh curren source power supply, he elecrcl rnsen cn be nore. Only he echncl rnsen nees o be consere. To sply he proble, le us conser n rc ype voce col oor supple by n el squre wve curren source uner no lo. The overnn equons o he syse re : v n v The nl conons re ssue o be zero,.e. v( ), n ( ) l Perornce - Wh Curren Source Supply (Con.) The ollown wveors llusre he response o n rc ype voce col oor uner squre wve curren source econ. v v v Perorce - Wh Vole Source Supply Wh n el vole source power supply, he response o n rc ype voce col oor cn be obne by solvn he se equons o he syse. When he echncl lo s ccoune or, he se equons us be solve nuerclly. I no echncl lo s ssue, however, nlycl soluon cn be obne. The overnn equons o he syse n hs cse re : R + n L L v L V N l n v n he ssue nl conons re ( ), v( ), n ( ) N l v

7 Perornce - Wh Vole Source Supply (Con.) The nlycl soluon o he oor uner squre wve vole source econ s: or <, E ( ) ( s s ) e e L s s v n v or, s, s ± 4 τ ( τω ) s A e e A s s s ( ) v v se se τ L R n ω L + n ( ) + v e e s s s s ( ) G n G Perornce - Wh Vole Source Supply (Con.) I s porn o noe h n v <. The col reverses s recon o oon. Thereore, hs ype o vole conrol s no use n sk rve pplcons s crucl h he col brn he R/W hes o spece rck n sy here urn ren n wrn. Perornce - Wh Vole Source Supply (Con.) In prcce, vole prole bse on he vole conrolle phse plne rjecory s use. Perornce - Iprovn Voce Col Moor Perorence by Shore-Turn In voce col oor, he ccelern orce on he ovn col s recly proporonl o he curren n he col. Thereore, he ser he curren rses, he ser he col woul respon. or hr sk rve, he ccess e woul be shorer. One wy o ccoplsh hs s o plce copper ube (shore urn) concenrc o he ovn col. l Copper Tube V R L e

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

Advanced Electromechanical Systems (ELE 847)

Advanced Electromechanical Systems (ELE 847) (ELE 847) Dr. Smr ouro-rener Topc 1.4: DC moor speed conrol Torono, 2009 Moor Speed Conrol (open loop conrol) Consder he followng crcu dgrm n V n V bn T1 T 5 T3 V dc r L AA e r f L FF f o V f V cn T 4

More information

Rotations.

Rotations. oons j.lbb@phscs.o.c.uk To s summ Fmes of efeence Invnce une nsfomons oon of wve funcon: -funcons Eule s ngles Emple: e e - - Angul momenum s oon geneo Genec nslons n Noehe s heoem Fmes of efeence Conse

More information

An object moving with speed v around a point at distance r, has an angular velocity. m/s m

An object moving with speed v around a point at distance r, has an angular velocity. m/s m Roion The mosphere roes wih he erh n moions wihin he mosphere clerly follow cure phs (cyclones, nicyclones, hurricnes, ornoes ec.) We nee o epress roion quniiely. For soli objec or ny mss h oes no isor

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

PHY2053 Summer C 2013 Exam 1 Solutions

PHY2053 Summer C 2013 Exam 1 Solutions PHY053 Sue C 03 E Soluon. The foce G on o G G The onl cobnon h e '/ = doubln.. The peed of lh le 8fulon c 86,8 le 60 n 60n h 4h d 4d fonh.80 fulon/ fonh 3. The dnce eled fo he ene p,, 36 (75n h 45 The

More information

II The Z Transform. Topics to be covered. 1. Introduction. 2. The Z transform. 3. Z transforms of elementary functions

II The Z Transform. Topics to be covered. 1. Introduction. 2. The Z transform. 3. Z transforms of elementary functions II The Z Trnsfor Tocs o e covered. Inroducon. The Z rnsfor 3. Z rnsfors of eleenry funcons 4. Proeres nd Theory of rnsfor 5. The nverse rnsfor 6. Z rnsfor for solvng dfference equons II. Inroducon The

More information

Supporting information How to concatenate the local attractors of subnetworks in the HPFP

Supporting information How to concatenate the local attractors of subnetworks in the HPFP n Effcen lgorh for Idenfyng Prry Phenoype rcors of Lrge-Scle Boolen Newor Sng-Mo Choo nd Kwng-Hyun Cho Depren of Mhecs Unversy of Ulsn Ulsn 446 Republc of Kore Depren of Bo nd Brn Engneerng Kore dvnced

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

OP = OO' + Ut + Vn + Wb. Material We Will Cover Today. Computer Vision Lecture 3. Multi-view Geometry I. Amnon Shashua

OP = OO' + Ut + Vn + Wb. Material We Will Cover Today. Computer Vision Lecture 3. Multi-view Geometry I. Amnon Shashua Comuer Vson 27 Lecure 3 Mul-vew Geomer I Amnon Shashua Maeral We Wll Cover oa he srucure of 3D->2D rojecon mar omograh Marces A rmer on rojecve geomer of he lane Eolar Geomer an Funamenal Mar ebrew Unvers

More information

Chapter 10. Simple Harmonic Motion and Elasticity. Goals for Chapter 10

Chapter 10. Simple Harmonic Motion and Elasticity. Goals for Chapter 10 Chper 0 Siple Hronic Moion nd Elsiciy Gols or Chper 0 o ollow periodic oion o sudy o siple hronic oion. o sole equions o siple hronic oion. o use he pendulu s prooypicl syse undergoing siple hronic oion.

More information

A Kalman filtering simulation

A Kalman filtering simulation A Klmn filering simulion The performnce of Klmn filering hs been esed on he bsis of wo differen dynmicl models, ssuming eiher moion wih consn elociy or wih consn ccelerion. The former is epeced o beer

More information

Chapter 36. a λ 2 2. (minima-dark fringes) Diffraction and the Wave Theory of Light. Diffraction by a Single Slit: Locating the Minima, Cont'd

Chapter 36. a λ 2 2. (minima-dark fringes) Diffraction and the Wave Theory of Light. Diffraction by a Single Slit: Locating the Minima, Cont'd Chpter 36 Diffrction In Chpter 35, we sw how light bes pssing through ifferent slits cn interfere with ech other n how be fter pssing through single slit flres-iffrcts- in Young's experient. Diffrction

More information

Forms of Energy. Mass = Energy. Page 1. SPH4U: Introduction to Work. Work & Energy. Particle Physics:

Forms of Energy. Mass = Energy. Page 1. SPH4U: Introduction to Work. Work & Energy. Particle Physics: SPH4U: Inroducion o ork ork & Energy ork & Energy Discussion Definiion Do Produc ork of consn force ork/kineic energy heore ork of uliple consn forces Coens One of he os iporn conceps in physics Alernive

More information

ISSN 075-7 : (7) 0 007 C ( ), E-l: ssolos@glco FPGA LUT FPGA EM : FPGA, LUT, EM,,, () FPGA (feldprogrble ge rrs) [, ] () [], () [] () [5] [6] FPGA LUT (Look-Up-Tbles) EM (Ebedded Meor locks) [7, 8] LUT

More information

MODEL SOLUTIONS TO IIT JEE ADVANCED 2014

MODEL SOLUTIONS TO IIT JEE ADVANCED 2014 MODEL SOLUTIONS TO IIT JEE ADVANCED Pper II Code PART I 6 7 8 9 B A A C D B D C C B 6 C B D D C A 7 8 9 C A B D. Rhc(Z ). Cu M. ZM Secon I K Z 8 Cu hc W mu hc 8 W + KE hc W + KE W + KE W + KE W + KE (KE

More information

FM Applications of Integration 1.Centroid of Area

FM Applications of Integration 1.Centroid of Area FM Applicions of Inegrion.Cenroid of Are The cenroid of ody is is geomeric cenre. For n ojec mde of uniform meril, he cenroid coincides wih he poin which he ody cn e suppored in perfecly lnced se ie, is

More information

Calculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( )

Calculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( ) Clculu 4, econ Lm/Connuy & Devve/Inel noe y Tm Plchow, wh domn o el Wh we hve o : veco-vlued uncon, ( ) ( ) ( ) j ( ) nume nd ne o veco The uncon, nd A w done wh eul uncon ( x) nd connuy e he componen

More information

4. Runge-Kutta Formula For Differential Equations

4. Runge-Kutta Formula For Differential Equations NCTU Deprme o Elecrcl d Compuer Egeerg 5 Sprg Course by Pro. Yo-Pg Ce. Ruge-Ku Formul For Derel Equos To solve e derel equos umerclly e mos useul ormul s clled Ruge-Ku ormul

More information

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse

More information

Physics 101 Lecture 4 Motion in 2D and 3D

Physics 101 Lecture 4 Motion in 2D and 3D Phsics 11 Lecure 4 Moion in D nd 3D Dr. Ali ÖVGÜN EMU Phsics Deprmen www.ogun.com Vecor nd is componens The componens re he legs of he righ ringle whose hpoenuse is A A A A A n ( θ ) A Acos( θ) A A A nd

More information

Caputo Equations in the frame of fractional operators with Mittag-Leffler kernels

Caputo Equations in the frame of fractional operators with Mittag-Leffler kernels nvenon Jounl o Reseh Tehnoloy n nneen & Mnemen JRTM SSN: 455-689 wwwjemom Volume ssue 0 ǁ Ooe 08 ǁ PP 9-45 Cuo uons n he me o onl oeos wh M-ele enels on Qn Chenmn Hou* Ynn Unvesy Jln Ynj 00 ASTRACT: n

More information

A, Electromagnetic Fields Final Exam December 14, 2001 Solution

A, Electromagnetic Fields Final Exam December 14, 2001 Solution 304-351, Electrognetic Fiels Finl Ex Deceer 14, 2001 Solution 1. e9.8. In chpter9.proles.extr.two loops, e of thin wire crry equl n opposite currents s shown in the figure elow. The rius of ech loop is

More information

10. A.C CIRCUITS. Theoretically current grows to maximum value after infinite time. But practically it grows to maximum after 5τ. Decay of current :

10. A.C CIRCUITS. Theoretically current grows to maximum value after infinite time. But practically it grows to maximum after 5τ. Decay of current : . A. IUITS Synopss : GOWTH OF UNT IN IUIT : d. When swch S s closed a =; = d. A me, curren = e 3. The consan / has dmensons of me and s called he nducve me consan ( τ ) of he crcu. 4. = τ; =.63, n one

More information

First-order piecewise-linear dynamic circuits

First-order piecewise-linear dynamic circuits Frs-order pecewse-lnear dynamc crcus. Fndng he soluon We wll sudy rs-order dynamc crcus composed o a nonlnear resse one-por, ermnaed eher by a lnear capacor or a lnear nducor (see Fg.. Nonlnear resse one-por

More information

Water Hammer in Pipes

Water Hammer in Pipes Waer Haer Hydraulcs and Hydraulc Machnes Waer Haer n Pes H Pressure wave A B If waer s flowng along a long e and s suddenly brough o res by he closng of a valve, or by any slar cause, here wll be a sudden

More information

PHYS 1443 Section 001 Lecture #4

PHYS 1443 Section 001 Lecture #4 PHYS 1443 Secon 001 Lecure #4 Monda, June 5, 006 Moon n Two Dmensons Moon under consan acceleraon Projecle Moon Mamum ranges and heghs Reerence Frames and relae moon Newon s Laws o Moon Force Newon s Law

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

e t dt e t dt = lim e t dt T (1 e T ) = 1

e t dt e t dt = lim e t dt T (1 e T ) = 1 Improper Inegrls There re wo ypes of improper inegrls - hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie

More information

Chapter 6 Plane Motion of Rigid Bodies

Chapter 6 Plane Motion of Rigid Bodies Chpe 6 Pne oon of Rd ode 6. Equon of oon fo Rd bod. 6., 6., 6.3 Conde d bod ced upon b ee een foce,, 3,. We cn ume h he bod mde of e numbe n of pce of m Δm (,,, n). Conden f he moon of he m cene of he

More information

4. Runge-Kutta Formula For Differential Equations. A. Euler Formula B. Runge-Kutta Formula C. An Example for Fourth-Order Runge-Kutta Formula

4. Runge-Kutta Formula For Differential Equations. A. Euler Formula B. Runge-Kutta Formula C. An Example for Fourth-Order Runge-Kutta Formula NCTU Deprme o Elecrcl d Compuer Egeerg Seor Course By Pro. Yo-Pg Ce. Ruge-Ku Formul For Derel Equos A. Euler Formul B. Ruge-Ku Formul C. A Emple or Four-Order Ruge-Ku Formul

More information

Using integration tables

Using integration tables Using integrtion tbles Integrtion tbles re inclue in most mth tetbooks, n vilble on the Internet. Using them is nother wy to evlute integrls. Sometimes the use is strightforwr; sometimes it tkes severl

More information

Response of MDOF systems

Response of MDOF systems Response of MDOF syses Degree of freedo DOF: he nu nuber of ndependen coordnaes requred o deerne copleely he posons of all pars of a syse a any nsan of e. wo DOF syses hree DOF syses he noral ode analyss

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

Calculate the efficiency associated with one rotation of the axle

Calculate the efficiency associated with one rotation of the axle We cn clculte the efficiency of one rottion of the xle by exining the work one. k Mx Your Rie: Workheet hi ctivity will tke you through the tep neee to optiize the work ue in your ouetrp cr. ollow thi

More information

Area Under the Torque vs. RPM Curve: Average Power

Area Under the Torque vs. RPM Curve: Average Power Are Uner the orque vs. RM Curve: Averge ower Wht is torque? Some Bsics Consier wrench on nut, the torque bout the nut is Force, F F θ r rf sinθ orque, If F is t right ngle to moment rm r then rf How oes

More information

CHAPTER 5: MULTIVARIATE METHODS

CHAPTER 5: MULTIVARIATE METHODS CHAPER 5: MULIVARIAE MEHODS Mulvarae Daa 3 Mulple measuremens (sensors) npus/feaures/arbues: -varae N nsances/observaons/eamples Each row s an eample Each column represens a feaure X a b correspons o he

More information

6. Gas dynamics. Ideal gases Speed of infinitesimal disturbances in still gas

6. Gas dynamics. Ideal gases Speed of infinitesimal disturbances in still gas 6. Gs dynmics Dr. Gergely Krisóf De. of Fluid echnics, BE Februry, 009. Seed of infiniesiml disurbnces in sill gs dv d, dv d, Coninuiy: ( dv)( ) dv omenum r r heorem: ( ( dv) ) d 3443 4 q m dv d dv llievi

More information

SOME USEFUL MATHEMATICS

SOME USEFUL MATHEMATICS SOME USEFU MAHEMAICS SOME USEFU MAHEMAICS I is esy o mesure n preic he behvior of n elecricl circui h conins only c volges n currens. However, mos useful elecricl signls h crry informion vry wih ime. Since

More information

Magnetostatics Bar Magnet. Magnetostatics Oersted s Experiment

Magnetostatics Bar Magnet. Magnetostatics Oersted s Experiment Mgneosics Br Mgne As fr bck s 4500 yers go, he Chinese discovered h cerin ypes of iron ore could rc ech oher nd cerin mels. Iron filings "mp" of br mgne s field Crefully suspended slivers of his mel were

More information

DEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS

DEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS 3 DEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS This chpter summrizes few properties of Cli ord Algebr nd describe its usefulness in e ecting vector rottions. 3.1 De nition of Associtive

More information

Parameter Estimation and Hypothesis Testing of Two Negative Binomial Distribution Population with Missing Data

Parameter Estimation and Hypothesis Testing of Two Negative Binomial Distribution Population with Missing Data Avlble ole wwwsceceeccom Physcs Poce 0 475 480 0 Ieol Cofeece o Mecl Physcs Bomecl ee Pmee smo Hyohess es of wo Neve Boml Dsbuo Poulo wh Mss D Zhwe Zho Collee of MhemcsJl Noml UvesyS Ch zhozhwe@6com Absc

More information

Physics Worksheet Lesson 4: Linear Motion Section: Name:

Physics Worksheet Lesson 4: Linear Motion Section: Name: Physics Workshee Lesson 4: Liner Moion Secion: Nme: 1. Relie Moion:. All moion is. b. is n rbirry coorine sysem wih reference o which he posiion or moion of somehing is escribe or physicl lws re formule.

More information

ECE Microwave Engineering

ECE Microwave Engineering EE 537-635 Microwve Engineering Adped from noes y Prof. Jeffery T. Willims Fll 8 Prof. Dvid R. Jcson Dep. of EE Noes Wveguiding Srucures Pr 7: Trnsverse Equivlen Newor (N) Wveguide Trnsmission Line Model

More information

ECE Microwave Engineering. Fall Prof. David R. Jackson Dept. of ECE. Notes 10. Waveguides Part 7: Transverse Equivalent Network (TEN)

ECE Microwave Engineering. Fall Prof. David R. Jackson Dept. of ECE. Notes 10. Waveguides Part 7: Transverse Equivalent Network (TEN) EE 537-635 Microwve Engineering Fll 7 Prof. Dvid R. Jcson Dep. of EE Noes Wveguides Pr 7: Trnsverse Equivlen Newor (N) Wveguide Trnsmission Line Model Our gol is o come up wih rnsmission line model for

More information

A capacitor consists of two conducting plates, separated by an insulator. Conduction plates: e.g., Aluminum foil Insulator: air, mica, ceramic, etc

A capacitor consists of two conducting plates, separated by an insulator. Conduction plates: e.g., Aluminum foil Insulator: air, mica, ceramic, etc 3//7 haper 6 apacors and Inducors Makng preparaon for dynamc crcus, whch hae far more applcaons han he sac crcus we hae learned so far. 6. apacors Sore energy n elecrc feld nsulaor onducng plaes A capacor

More information

THIS PAGE DECLASSIFIED IAW EO 12958

THIS PAGE DECLASSIFIED IAW EO 12958 THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW EO 2958 THIS PAGE DECLASSIFIED IAW E0 2958 S T T T I R F R S T Exhb e 3 9 ( 66 h Bm dn ) c f o 6 8 b o d o L) B C = 6 h oup C L) TO d 8 f f

More information

Stat 6863-Handout 5 Fundamentals of Interest July 2010, Maurice A. Geraghty

Stat 6863-Handout 5 Fundamentals of Interest July 2010, Maurice A. Geraghty S 6863-Hou 5 Fuels of Ieres July 00, Murce A. Gerghy The pror hous resse beef cl occurreces, ous, ol cls e-ulero s ro rbles. The fl copoe of he curl oel oles he ecooc ssupos such s re of reur o sses flo.

More information

T-Match: Matching Techniques For Driving Yagi-Uda Antennas: T-Match. 2a s. Z in. (Sections 9.5 & 9.7 of Balanis)

T-Match: Matching Techniques For Driving Yagi-Uda Antennas: T-Match. 2a s. Z in. (Sections 9.5 & 9.7 of Balanis) 3/0/018 _mch.doc Pge 1 of 6 T-Mch: Mching Techniques For Driving Ygi-Ud Anenns: T-Mch (Secions 9.5 & 9.7 of Blnis) l s l / l / in The T-Mch is shun-mching echnique h cn be used o feed he driven elemen

More information

Interval Estimation. Consider a random variable X with a mean of X. Let X be distributed as X X

Interval Estimation. Consider a random variable X with a mean of X. Let X be distributed as X X ECON 37: Ecoomercs Hypohess Tesg Iervl Esmo Wh we hve doe so fr s o udersd how we c ob esmors of ecoomcs reloshp we wsh o sudy. The queso s how comforble re we wh our esmors? We frs exme how o produce

More information

Chapter 4: Motion in Two Dimensions Part-1

Chapter 4: Motion in Two Dimensions Part-1 Lecue 4: Moon n Two Dmensons Chpe 4: Moon n Two Dmensons P- In hs lesson we wll dscuss moon n wo dmensons. In wo dmensons, s necess o use eco noon o descbe phscl qunes wh boh mnude nd decon. In hs chpe,

More information

Periodic motions of a class of forced infinite lattices with nearest neighbor interaction

Periodic motions of a class of forced infinite lattices with nearest neighbor interaction J. Mah. Anal. Appl. 34 28 44 52 www.elsever.co/locae/jaa Peroc oons of a class of force nfne laces wh neares neghbor neracon Chao Wang a,b,, Dngban Qan a a School of Maheacal Scence, Suzhou Unversy, Suzhou

More information

I I M O I S K J H G. b gb g. Chapter 8. Problem Solutions. Semiconductor Physics and Devices: Basic Principles, 3 rd edition Chapter 8

I I M O I S K J H G. b gb g. Chapter 8. Problem Solutions. Semiconductor Physics and Devices: Basic Principles, 3 rd edition Chapter 8 emcouc hyscs evces: Bsc rcles, r eo Cher 8 oluos ul rolem oluos Cher 8 rolem oluos 8. he fwr s e ex f The e ex f e e f ex () () f f f f l G e f f ex f 59.9 m 60 m 0 9. m m 8. e ex we c wre hs s e ex h

More information

Homework 8: Rigid Body Dynamics Due Friday April 21, 2017

Homework 8: Rigid Body Dynamics Due Friday April 21, 2017 EN40: Dynacs and Vbraons Hoework 8: gd Body Dynacs Due Frday Aprl 1, 017 School of Engneerng Brown Unversy 1. The earh s roaon rae has been esaed o decrease so as o ncrease he lengh of a day a a rae of

More information

1.B Appendix to Chapter 1

1.B Appendix to Chapter 1 Secon.B.B Append o Chper.B. The Ordnr Clcl Here re led ome mporn concep rom he ordnr clcl. The Dervve Conder ncon o one ndependen vrble. The dervve o dened b d d lm lm.b. where he ncremen n de o n ncremen

More information

P-Convexity Property in Musielak-Orlicz Function Space of Bohner Type

P-Convexity Property in Musielak-Orlicz Function Space of Bohner Type J N Sce & Mh Res Vol 3 No (7) -7 Alble ole h://orlwlsogocd/deh/sr P-Coey Proery Msel-Orlcz Fco Sce o Boher ye Yl Rodsr Mhecs Edco Deree Fcly o Ss d echology Uerss sl Neger Wlsogo Cerl Jdoes Absrcs Corresodg

More information

Physics 201 Lecture 2

Physics 201 Lecture 2 Physcs 1 Lecure Lecure Chper.1-. Dene Poson, Dsplcemen & Dsnce Dsngush Tme nd Tme Inerl Dene Velocy (Aerge nd Insnneous), Speed Dene Acceleron Undersnd lgebrclly, hrough ecors, nd grphclly he relonshps

More information

In the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!

In the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!) i+1,q - [(! ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal

More information

Reconstruction of transient vibration and sound radiation of an impacted plate

Reconstruction of transient vibration and sound radiation of an impacted plate INTE-NOIE 06 econsrucon of rnsen vbron nd sound rdon of n mpced ple Ln en ; Chun-Xn B ; Xo-Zhen Zhn ; Yon-Bn Zhn 4 ; Ln Xu 5,,,4,5 Insue of ound nd Vbron eserch, efe Unversy of Technoloy, 9 Tunx od, efe

More information

Exponents and Powers

Exponents and Powers EXPONENTS AND POWERS 9 Exponents nd Powers CHAPTER. Introduction Do you know? Mss of erth is 5,970,000,000,000, 000, 000, 000, 000 kg. We hve lredy lernt in erlier clss how to write such lrge nubers ore

More information

Lesson 2 Transmission Lines Fundamentals

Lesson 2 Transmission Lines Fundamentals Lesson Transmsson Lnes Funamenals 楊尚達 Shang-Da Yang Insue of Phooncs Technologes Deparmen of Elecrcal Engneerng Naonal Tsng Hua Unersy Tawan Sec. -1 Inroucon 1. Why o scuss TX lnes srbue crcus?. Crera

More information

MATH 124 AND 125 FINAL EXAM REVIEW PACKET (Revised spring 2008)

MATH 124 AND 125 FINAL EXAM REVIEW PACKET (Revised spring 2008) MATH 14 AND 15 FINAL EXAM REVIEW PACKET (Revised spring 8) The following quesions cn be used s review for Mh 14/ 15 These quesions re no cul smples of quesions h will pper on he finl em, bu hey will provide

More information

Chapter 1: Logarithmic functions and indices

Chapter 1: Logarithmic functions and indices Chpter : Logrithmic functions nd indices. You cn simplify epressions y using rules of indices m n m n m n m n ( m ) n mn m m m m n m m n Emple Simplify these epressions: 5 r r c 4 4 d 6 5 e ( ) f ( ) 4

More information

Electromagnetic Transient Simulation of Large Power Transformer Internal Fault

Electromagnetic Transient Simulation of Large Power Transformer Internal Fault Inernonl Conference on Advnces n Energy nd Envronmenl Scence (ICAEES 5) Elecromgnec Trnsen Smulon of rge Power Trnsformer Inernl Ful Jun u,, Shwu Xo,, Qngsen Sun,c, Huxng Wng,d nd e Yng,e School of Elecrcl

More information

mywbut.com Lesson 13 Representation of Sinusoidal Signal by a Phasor and Solution of Current in R-L-C Series Circuits

mywbut.com Lesson 13 Representation of Sinusoidal Signal by a Phasor and Solution of Current in R-L-C Series Circuits wut.co Lesson 3 Representtion of Sinusoil Signl Phsor n Solution of Current in R-L-C Series Circuits wut.co In the lst lesson, two points were escrie:. How sinusoil voltge wvefor (c) is generte?. How the

More information

ON DISTORTION ENERGY THEORY IN HIGH CYCLE MULTI-AXIAL FATIGUE

ON DISTORTION ENERGY THEORY IN HIGH CYCLE MULTI-AXIAL FATIGUE Inernonl Journl o Mechncl Engneerng n Technology (IJMET) Volue 9, Issue 7, July 018, pp. 140 154, Arcle ID: IJMET_09_07_15 Avlble onlne hp://www.ee.co/je/ssues.sp?jtype=ijmet&vtype=9&itype=7 ISSN Prn:

More information

Lecture 8: Camera Calibra0on

Lecture 8: Camera Calibra0on Lecture 8: Cer Clbron rofessor Fe- Fe L Stnford Vson Lb Lecture 8 -! Wht we wll lern tody? Revew cer preters Affne cer odel (roble Set (Q4)) Cer clbron Vnshng ponts nd lnes (roble Set (Q)) Redng: [F] Chpter

More information

This is an example to show you how SMath can calculate the movement of kinematic mechanisms.

This is an example to show you how SMath can calculate the movement of kinematic mechanisms. Dec :5:6 - Kinemaics model of Simple Arm.sm This file is provided for educaional purposes as guidance for he use of he sofware ool. I is no guaraeed o be free from errors or ommissions. The mehods and

More information

Jordan Journal of Physics

Jordan Journal of Physics Volume, Number, 00. pp. 47-54 RTICLE Jordn Journl of Physcs Frconl Cnoncl Qunzon of he Free Elecromgnec Lgrngn ensy E. K. Jrd, R. S. w b nd J. M. Khlfeh eprmen of Physcs, Unversy of Jordn, 94 mmn, Jordn.

More information

Determining robot s maximum dynamic load carrying capacity in point-to-point motion by applying limitation of joints torque

Determining robot s maximum dynamic load carrying capacity in point-to-point motion by applying limitation of joints torque Globl Journl o Scenc Reserches Avlble onlne gjsr.blue-.org GJSR Journl. Vol.. - June E-ISSN: -7 Deernng robo s u ync lo crryng ccy n on-o-on oon by lyng lon o jons orue H. R. She M. Bhr A. Kl E n A. M.

More information

Including the ordinary differential of distance with time as velocity makes a system of ordinary differential equations.

Including the ordinary differential of distance with time as velocity makes a system of ordinary differential equations. Soluons o Ordnary Derenal Equaons An ordnary derenal equaon has only one ndependen varable. A sysem o ordnary derenal equaons consss o several derenal equaons each wh he same ndependen varable. An eample

More information

September 20 Homework Solutions

September 20 Homework Solutions College of Engineering nd Compuer Science Mechnicl Engineering Deprmen Mechnicl Engineering A Seminr in Engineering Anlysis Fll 7 Number 66 Insrucor: Lrry Creo Sepember Homework Soluions Find he specrum

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

More information

Physics 3 (PHYF144) Chap 3: The Kinetic Theory of Gases - 1

Physics 3 (PHYF144) Chap 3: The Kinetic Theory of Gases - 1 Physcs (PYF44) ha : he nec heory of Gases -. Molecular Moel of an Ieal Gas he goal of he olecular oel of an eal gas s o unersan he acroscoc roeres (such as ressure an eeraure ) of gas n e of s croscoc

More information

On Fractional Operational Calculus pertaining to the product of H- functions

On Fractional Operational Calculus pertaining to the product of H- functions nenonl eh ounl of Enneen n ehnolo RE e-ssn: 2395-56 Volume: 2 ue: 3 une-25 wwwene -SSN: 2395-72 On Fonl Oeonl Clulu enn o he ou of - funon D VBL Chu, C A 2 Demen of hem, Unve of Rhn, u-3255, n E-ml : vl@hooom

More information

Characteristic Function for the Truncated Triangular Distribution., Myron Katzoff and Rahul A. Parsa

Characteristic Function for the Truncated Triangular Distribution., Myron Katzoff and Rahul A. Parsa Secion on Survey Reserch Mehos JSM 009 Chrcerisic Funcion for he Trunce Tringulr Disriuion Jy J. Kim 1 1, Myron Kzoff n Rhul A. Prs 1 Nionl Cener for Helh Sisics, 11Toleo Ro, Hysville, MD. 078 College

More information

The Characterization of Jones Polynomial. for Some Knots

The Characterization of Jones Polynomial. for Some Knots Inernon Mhemc Forum,, 8, no, 9 - The Chrceron of Jones Poynom for Some Knos Mur Cncn Yuuncu Y Ünversy, Fcuy of rs nd Scences Mhemcs Deprmen, 8, n, Turkey m_cencen@yhoocom İsm Yr Non Educon Mnsry, 8, n,

More information

Lecture 12: HEMT AC Properties

Lecture 12: HEMT AC Properties Lecure : HEMT A Proeres Quas-sac oeraon Transcaacances -araeers Non-quas ac effecs Parasc ressances / caacancs f f ax ean ue for aer 6: 7-86 95-407 {407-46 sk MEFET ars} 47-44. (.e. sk an MEFET ars brefl

More information

Homework 2 Solutions

Homework 2 Solutions Mah 308 Differenial Equaions Fall 2002 & 2. See he las page. Hoework 2 Soluions 3a). Newon s secon law of oion says ha a = F, an we know a =, so we have = F. One par of he force is graviy, g. However,

More information

Nanoparticles. Educts. Nucleus formation. Nucleus. Growth. Primary particle. Agglomeration Deagglomeration. Agglomerate

Nanoparticles. Educts. Nucleus formation. Nucleus. Growth. Primary particle. Agglomeration Deagglomeration. Agglomerate ucs Nucleus Nucleus omaon cal supesauaon Mng o eucs, empeaue, ec. Pmay pacle Gowh Inegaon o uson-lme pacle gowh Nanopacles Agglomeaon eagglomeaon Agglomeae Sablsaon o he nanopacles agans agglomeaon! anspo

More information

S Radio transmission and network access Exercise 1-2

S Radio transmission and network access Exercise 1-2 S-7.330 Rdio rnsmission nd nework ccess Exercise 1 - P1 In four-symbol digil sysem wih eqully probble symbols he pulses in he figure re used in rnsmission over AWGN-chnnel. s () s () s () s () 1 3 4 )

More information

1. Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor.

1. Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor. In Eercise 1, use sndrd recngulr Cresin coordine sysem. Le ime be represened long he horizonl is. Assume ll ccelerions nd decelerions re consn. 1. Consider PSA iniilly res in he beginning of he lef-hnd

More information

Executive Committee and Officers ( )

Executive Committee and Officers ( ) Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r

More information

ENGR 1990 Engineering Mathematics The Integral of a Function as a Function

ENGR 1990 Engineering Mathematics The Integral of a Function as a Function ENGR 1990 Engineering Mhemics The Inegrl of Funcion s Funcion Previously, we lerned how o esime he inegrl of funcion f( ) over some inervl y dding he res of finie se of rpezoids h represen he re under

More information

DC Machines. Introduction - commutation. Commutation. I. Introduction Electrical Energy Technology

DC Machines. Introduction - commutation. Commutation. I. Introduction Electrical Energy Technology UNVERSTY OF TECHNOLOGY, SYDNEY FACULTY OF ENGNEERNG 48550 Electricl Enery Technoloy DC Mchines Topics to cover: 1. ntroduction 2. EMF & Torque 3. Equivlent Circuit 4. Perornce. ntroduction Principle o

More information

Measurement of Transmission Loss of Materials Using a Standing Wave Tube

Measurement of Transmission Loss of Materials Using a Standing Wave Tube urue University urue e-us ulictions of the Ry W. Herrick Lortories School of Mechnicl Engineering -6 Mesurement of rnsmission Loss of Mterils Using Stning Wve ue J Sturt Bolton urue University, olton@purue.eu

More information

Physics 120 Spring 2007 Exam #1 April 20, Name

Physics 120 Spring 2007 Exam #1 April 20, Name Phc 0 Spng 007 E # pl 0, 007 Ne P Mulple Choce / 0 Poble # / 0 Poble # / 0 Poble # / 0 ol / 00 In eepng wh he Unon College polc on cdec hone, ued h ou wll nehe ccep no pode unuhozed nce n he copleon o

More information

Chapter 2. Motion along a straight line. 9/9/2015 Physics 218

Chapter 2. Motion along a straight line. 9/9/2015 Physics 218 Chper Moion long srigh line 9/9/05 Physics 8 Gols for Chper How o describe srigh line moion in erms of displcemen nd erge elociy. The mening of insnneous elociy nd speed. Aerge elociy/insnneous elociy

More information

X Fx = F A. If applied force is small, book does not move (static), a x =0, then f=f s

X Fx = F A. If applied force is small, book does not move (static), a x =0, then f=f s A Appl ewton s nd Lw X 0 X A I pplied orce is sll, boo does not ove sttic, 0, then s A Increse pplied orce, boo still does not ove Increse A ore, now boo oves, 0 > A A here is soe iu sttic rictionl orce,

More information

Week 8 Lecture 3: Problems 49, 50 Fourier analysis Courseware pp (don t look at French very confusing look in the Courseware instead)

Week 8 Lecture 3: Problems 49, 50 Fourier analysis Courseware pp (don t look at French very confusing look in the Courseware instead) Week 8 Lecure 3: Problems 49, 5 Fourier lysis Coursewre pp 6-7 (do look Frech very cofusig look i he Coursewre ised) Fourier lysis ivolves ddig wves d heir hrmoics, so i would hve urlly followed fer he

More information

Algebra Of Matrices & Determinants

Algebra Of Matrices & Determinants lgebr Of Mtrices & Determinnts Importnt erms Definitions & Formule 0 Mtrix - bsic introduction: mtrix hving m rows nd n columns is clled mtrix of order m n (red s m b n mtrix) nd mtrix of order lso in

More information

Physics Dynamics: Atwood Machine

Physics Dynamics: Atwood Machine plce of ind F A C U L Y O F E D U C A I O N Deprtent of Curriculu nd Pedoy Physics Dynics: Atwood Mchine Science nd Mthetics Eduction Reserch Group Supported by UBC echin nd Lernin Enhnceent Fund 0-04

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

( ) ( ) ( ) 0. Conservation of Energy & Poynting Theorem. From Maxwell s equations we have. M t. From above it can be shown (HW)

( ) ( ) ( ) 0. Conservation of Energy & Poynting Theorem. From Maxwell s equations we have. M t. From above it can be shown (HW) 8 Conson o n & Ponn To Fo wll s quons w D B σ σ Fo bo n b sown (W) o s W w bo on o s l us n su su ul ow ns [W/ ] [W] su P su B W W 4 444 s W A A s V A A : W W R o n o so n n: [/s W] W W 4 44 9 W : W F

More information

Chapter 2 Linear Mo on

Chapter 2 Linear Mo on Chper Lner M n .1 Aerge Velcy The erge elcy prcle s dened s The erge elcy depends nly n he nl nd he nl psns he prcle. Ths mens h prcle srs rm pn nd reurn bck he sme pn, s dsplcemen, nd s s erge elcy s

More information

Average & instantaneous velocity and acceleration Motion with constant acceleration

Average & instantaneous velocity and acceleration Motion with constant acceleration Physics 7: Lecure Reminders Discussion nd Lb secions sr meeing ne week Fill ou Pink dd/drop form if you need o swich o differen secion h is FULL. Do i TODAY. Homework Ch. : 5, 7,, 3,, nd 6 Ch.: 6,, 3 Submission

More information

Solution in semi infinite diffusion couples (error function analysis)

Solution in semi infinite diffusion couples (error function analysis) Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of

More information

4.8 Improper Integrals

4.8 Improper Integrals 4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls

More information

Solutions to Problems from Chapter 2

Solutions to Problems from Chapter 2 Soluions o Problems rom Chper Problem. The signls u() :5sgn(), u () :5sgn(), nd u h () :5sgn() re ploed respecively in Figures.,b,c. Noe h u h () :5sgn() :5; 8 including, bu u () :5sgn() is undeined..5

More information

sec x over the interval (, ). x ) dx dx x 14. Use a graphing utility to generate some representative integral curves of the function Curve on 5

sec x over the interval (, ). x ) dx dx x 14. Use a graphing utility to generate some representative integral curves of the function Curve on 5 Curve on Clcultor eperience Fin n ownlo (or type in) progrm on your clcultor tht will fin the re uner curve using given number of rectngles. Mke sure tht the progrm fins LRAM, RRAM, n MRAM. (You nee to

More information