TEST-12 TOPIC : SHM and WAVES
|
|
- Dorcas Parks
- 5 years ago
- Views:
Transcription
1 Q. Four sprig coec wih ss s show i figure. Fid frequecy of S.H.. TEST- TOPIC : SH d WVES 4 7 (D) These wo coeced i series. So = = Now ll re i prllel so eq = 4 so freq. = Q. sll ss execue S.H.. bou poi O wih pliude & ie period T. Is T displcee fer ie fro e posiio 8 is- (D) 8 [D] eq. of S.H.. x = si T so = 8 x = Q.3 uifor rod of legh.0 is suspeded hrough ed & oscille wih sll pliude. The ie period is -.60 s.80 s.00 s (D).40 s [D] T = I0 h gh where I 0 = / h = So T =.40 s Q.4 Four siple hroic ibrios x = 8 si, x = 6si ( + /), x 3 = 4 si ( + ) d x 4 = si ( + 3/) re superiposed o ech oher. The resulig pliude d is phse differece wih x re respeciely - [D] 0, 0, () 4 (D) 4,, 4 Q.5 O sooh iclied ple body of ss is [] ched bewee wo sprigs. The oher eds of he sprigs re fixed o fir suppors. If ech sprig hs force cos, he period of oscillio of he body is (ssuig he sprig s ssless) - si (D) si Pge of 8
2 Q.6 The ccelerio-displcee (-x) grph of pricle execuig siple oio is show i figure. The frequecy of oscillio is gie by - (c/s ) 0.5 s 5s [] = 0 x = 0 = 0 0 x (c) 0s (D) 0s = 0 Q.7 pricle execues SH of pliude 5 c d period 3s. The elociy of he pricle disce 4 c fro he e posiio - 8 c/s c/s 4 c/s (D) 6 c/s [D] V = = 3 3 x = x T 5 6 = 6 c/s Q.8 If he legh of pedulu is de 9 ies d ss of he bob is de 4 ies, he he lue of ie period becoes - 3 T 3/ T 4 T (D) T [] Tie period does o deped o ss T. (i), T 9.(ii) or T = 3 T. Q.9 The legh of siple pedulu execuig SH is icresed by %. The percege icrese i he ie period of he pedulu is - 0% % % (D) 4 % [] T T = T = T 00 0 T 00 % = 00 % = 0% T 0 Q.0 uifor sprig of orl legh hs force cos. I is cu io wo pieces of leghs, d such h = where is ieger. The he lue of (force cos of sprig of legh ) is - ( ) ( ) = = ( + ) = ( ) ( ) (D) ( ) or = ( ) or = Q. syse show i figure, cosiss of ssless pulley, sprig of force cos d bloc of ss. If bloc is jus slighly displced ericlly dow fro is equilibriu posiio d relesed, he he period of ericl oscillios is T = T = 4 Displcee i box = x displcee i box = x F = x F = F F = 4 x T = 4 T = (D) T = 4 3 Q. Four sprigs & ss is coeced s show i figure. If ss is displced horizolly he wh is he frequecy of S.H..? F F x F Pge of 8
3 4 7 Coeced i series so eq so ow Now ll i prllel so eq = + + = 4 & so frequecy f = 4 (D) 4 7 Q. 3 Vriio of pliude of ibrios s fucio of ie show s grph is- 0 ( ) or = Q.4 pricle of ss is ched o hree ideicl sprigs, B d C ech of force cos s show i figure. If he pricle of ss is pushed slighly gis he sprig d relesed, he he ie period of oscillio is - T = B O ( cos C ) (D) = ( cos 45) = 3 Q.5 siple pedulu wih is bob (ss ) chrged wih +q oscilles i uifor elecric field E, s show i he figure he period of oscillio shll be +q 0 0 (D) 0 g / g qe / g qe / E (uifor) / / [C]. q (D) ge / / [C] Pge 3 of 8
4 Q.6 Which of he followig digrs correcly rele displcee, elociy d ccelerio wih ie for pricle execuig SH - PE I II () y (b) y T/ PE III IV y (c) (d) y [] Q.7 Boh he equios y = si d. y = si + cos represe S.H.. The rio of he pliudes of he wo oios is- 0.5 (D) [D] Q.8 siple pedulu hs ie period T whe o he erh s surfce, d T whe e o heigh R boe he erh s surfce, where R is he rdius of he erh. The lue of T / T is - [IIT-00] 4 (D) [D] I d III II d IV II d III (D) I d IV Q. Tie period of siple pedulu is T. Whe poi of suspesio of he pedulu is oig upwrd followig he equio y = (where = /s, y is he displcee of poi of suspesio) is ie period becoes T, he - [IIT-005] T 5 = T 6 x T 6 = T 5 T T = (D) 4 = T T 5 Q. I he syse show if he iexesible srig coecig d is cu, he ccelerios of ss d re - [IIT-006] Q.9 pricle execues siple hroic oio bewee x = d x = +. The ie e for i o go fro 0 o / is T d o go fro / o is T.The - [IIT-00] T < T T > T T = T (D) T = T [] Q.0 For pricle execuig SH he displcee x is gie by x = cos. Ideify he grph which represes he riio of poeil eergy (PE) s fucio of ie d displcee x - [IIT-003] g, g srig g, g g, g (D) g, g Q.3 source of frequecy 'f ' is siory d obserer srs oig owrds i = 0 wih Pge 4 of 8
5 cos sll ccelerio. The he riio of obsered frequecy f ' resisered by he obserer wih ie is bes represeed s - f ' f ' The seprio bewee he source d liseer will be icresig (D) The seprio bewee source d he liseer is decresig [D] [] f 0 f ' 0 f s (D) f ' ( )f Q.4 perso P is 600 wy fro he sio whe ri is pprochig sio wih 7 /h, i blows whisle of frequecy 800 Hz whe 800 wy fro he sio. Fid he frequecy herd by he perso. Speed of soud = 340 s Hz 89.5 Hz s 800 pp = = cos s s cos s S 600 P Hz (D) Hz = Q.5 If he ppre frequecy of soud herd by he obserer is ore h he cul frequecy he- The liseer will be oig wy fro source The source will be oig wy fro liseer Q.6 ppre frequecy of ri is herd by obserer i ri B s 3/4 of he rue frequecy. Fid he lue of elociy of ri B i /sec. ig ri o be siory. If he soud elociy is 33 /sec (D) 83 [D] Q.7 police cr oig /s, chses oorcyclis. The police souds his hor 76 Hz, while boh of he oe owrds siory sire of frequecy 65 Hz. Clcule he speed of he oorcycle, if i is gie h he does o obseres y bes. 33 /s /s [IIT - 003] zero (D) /s Q.8 oor cycle srs fro res d cceleres log srigh ph /s. he srig poi of he oor cycle here is siory elecric sire. How fr hs he oor cycle goe whe he drier hers he frequecy of he sire 94% of is lue whe he oor cycle ws res? (Speed of soud = 330 s ) [IEEE-009] (D) 96 Whe source i siory d obserer is oig wy fro he source. ' = V 0 V V 330 V = 330 V 0 = 9.8 /s V 0 = 0 + s Pge 5 of 8
6 0 V S = = = 98. Q.9 The equio of we disurbce is gie s : y = 0.0 cos 50 cos (0x), where x d 5 [C] w = 50, y re i eres d i secods. Choose he wrog see - iode occurs x = 0.3 The welegh is 0. The speed of he cosiue wes is 4 /s (D) Node occurs x = 0.5 = 0 = w = 5 /sec Q.30 The rio of iesiies bewee wo cohere soud source is 4 :. The differece of loudess i decibels (db) bewee xiu d iiu iesiies, whe hey ierfere i spce is - 0 log 0 log 3 0 log 3 (D) 0 log I I 4 = = = So 3 I = So x 9 I = L = 0 log x Ii Ii = 0 log 3 Q.3 Two wes re represeed by y = si d y = cos 6 Wh will be heir resul pliude? = 0 log 9 3 (D) [C] Q.3 The speed of rserse ibrios i sreched srig is 700 c/s. If he srig is log, he frequecy wih which i resoes i fudel ode is - 7 Hz 4 Hz L = 4 7 Hz (D) 7 Hz = L & = = 4 7 Hz Q.33 Whe wo wes of los equl frequecies d re produced siuleously, he he ie ierl bewee successie xi is - (D) x T x T = x Q.34 For he siory we y = 4si 5 [] cos (96), he disce bewee ode d he ex iode is : (D) 30 [] Q.35 ibrig uig for of frequecy is plced er he ope ed of log cylidricl ube. Er The ube hs side opeig d is lso fied wih oble reflecig piso. s he piso is oed hrough 8.75 c, he iesiy of soud chges fro xiu o iiu. If he speed of soud is 350 ere per secod, he is 500 Hz 000 Hz 000 Hz (D) 4000 Hz Q.36 uig for of ow frequecy 56 Hz es 5 bes per secod wih he ibrig srig of pio. The be frequecy decreses o bes per secod whe he esio i he pio srig is Pge 6 of 8
7 slighly icresed. The frequecy of he pio srig before icresig he esio ws 56 Hz [IEEE-003] 56 5 Hz Hz (D) 56 + Hz Q.37 srig is sreched bewee fixed pois sepred by 75.0 c. I is obsered o he reso frequecies of 40 Hz d 35 Hz. There re o oher reso frequecies bewee hese wo. The, he lowes reso frequecy for his srig is [IEEE 006] 050 Hz 0.5 Hz 05 Hz (D).05 Hz [C] Q.38 we rellig log he x- xis is described by he equio y(x,) = cos (x ). If he welegh d he ie period of he we re 0.08 d.0 s, respeciely, he d i pproprie uis re [IEEE 008] = = , =.0. 0, = =.50 =.0 (D) = 5.00 = [D] Q.39 Two ideicl srigh wires re sreched so s o produce 6 bes per secod whe ibrig siuleously. O chgig he esio slighly i oe of he, he be frequecy reis uchged. Deoig by T, T he higher d he lower iiil esios i he srigs, he i could be sid h while ig he boe chges i esio - T ws decresed T ws icresed [IIT 99] T ws icresed (D) Nohig c be sid Q.40 The displcee y of pricle execuig periodic oio is gie by y = cos ( ) si (000 ) This expressio y be cosidered o be resul of he superposiio of idepede hroic oios wo hree [IIT 99] four (D) fie Q.4 The exesio i srig, obeyig Hooe s lw is x. The speed of soud i he srig is. If he exesio i he srig is icresed o.5 x, he speed of soud will be [IIT 996].50 (D) 0.75 [] Q.4 rellig we i sreched srig is described by he equio y = si(x ). The xiu pricle elociy is [IIT 997] / d/d (D) x/ [] Q.43 rserse siusoidl we of pliude, welegh d frequecy f is rellig o sreched srig. The xiu speed of y poi o he srig is /0, where is he speed of propgio of he we. If = 0 3 d = 0 s, he is gie by- [IIT 998] = 0 = 0 3 = 0 3 /() (D) = 0 4 [] Q.44 Sdig wes c be produced- [IIT 999] o srig clped boh he eds Pge 7 of 8
8 o srig clped oe ed d free he oher whe icide we ges refleced fro wll (D) ll of hese [D] Q.45 I we oio y = si (x - ), y c represe- [IIT 999] elecric field geic field displcee (D) ll of hese [D] Pge 8 of 8
Physics 232 Exam I Feb. 13, 2006
Phsics I Fe. 6 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio. The oio hs peiod o.59 secods. iiil ie i is oud o e 8.66 c o he igh o he equiliiu posiio d oig o he le wih eloci o sec.
More information1. Six acceleration vectors are shown for the car whose velocity vector is directed forward. For each acceleration vector describe in words the
Si ccelerio ecors re show for he cr whose eloci ecor is direced forwrd For ech ccelerio ecor describe i words he iseous moio of he cr A ri eers cured horizol secio of rck speed of 00 km/h d slows dow wih
More informationPhysics 232 Exam I Feb. 14, 2005
Phsics I Fe., 5 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio wih gul eloci o dissec. gie is i ie i is oud o e 8 c o he igh o he equiliiu posiio d oig o he le wih eloci o.5 sec..
More informationWeek 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 informationLEADER & ACHIEVER COURSE PHASE : MLA,MLB,MLC, MLD, MLE,MLF, MLG, MLH, MLI, MLJ, MAZA,MAZB & MAZC TARGET : PRE-MEDICAL 2016
CSSRM CNTCT PRGRMME (cdeic Sessio : 05-06) EDER & CIEVER CURSE PSE : M,M,MC, MD, ME,MF, MG, M, MI, MJ, MZ,MZ & MZC Tes Type : MJR TRGET : PRE-MEDIC 06 Tes Per : IPMT TEST DTE : 07-04 - 06 TEST SYUS : SYUS
More informationOne of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of
Oe of he commo descipios of cuilie moio uses ph ibles, which e mesuemes mde log he ge d oml o he ph of he picles. d e wo ohogol xes cosideed sepely fo eey is of moio. These coodies poide ul descipio fo
More information(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1.
Answers o Een Numbered Problems Chper. () 7 m s, 6 m s (b) 8 5 yr 4.. m ih 6. () 5. m s (b).5 m s (c).5 m s (d) 3.33 m s (e) 8. ().3 min (b) 64 mi..3 h. ().3 s (b) 3 m 4..8 mi wes of he flgpole 6. (b)
More informationMotion in a Straight Line
Moion in Srigh Line. Preei reched he mero sion nd found h he esclor ws no working. She wlked up he sionry esclor in ime. On oher dys, if she remins sionry on he moing esclor, hen he esclor kes her up in
More information1. 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 informationChapter 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 informationF.Y. Diploma : Sem. II [CE/CR/CS] Applied Mathematics
F.Y. Diplom : Sem. II [CE/CR/CS] Applied Mhemics Prelim Quesio Pper Soluio Q. Aemp y FIVE of he followig : [0] Q. () Defie Eve d odd fucios. [] As.: A fucio f() is sid o e eve fucio if f() f() A fucio
More informationPHYSICS 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 informationP441 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 informationN! AND THE GAMMA FUNCTION
N! AND THE GAMMA FUNCTION Cosider he produc of he firs posiive iegers- 3 4 5 6 (-) =! Oe calls his produc he facorial ad has ha produc of he firs five iegers equals 5!=0. Direcly relaed o he discree! fucio
More informationReinforcement Learning
Reiforceme Corol lerig Corol polices h choose opiml cios Q lerig Covergece Chper 13 Reiforceme 1 Corol Cosider lerig o choose cios, e.g., Robo lerig o dock o bery chrger o choose cios o opimize fcory oupu
More informationForms 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 informationEnergy Density / Energy Flux / Total Energy in 1D. Key Mathematics: density, flux, and the continuity equation.
ecure Phys 375 Eergy Desiy / Eergy Flu / oal Eergy i D Overview ad Moivaio: Fro your sudy of waves i iroducory physics you should be aware ha waves ca raspor eergy fro oe place o aoher cosider he geeraio
More informationFresnel Dragging Explained
Fresel Draggig Explaied 07/05/008 Decla Traill Decla@espace.e.au The Fresel Draggig Coefficie required o explai he resul of he Fizeau experime ca be easily explaied by usig he priciples of Eergy Field
More information2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information.
Nme D Moion WS The equions of moion h rele o projeciles were discussed in he Projecile Moion Anlsis Acii. ou found h projecile moes wih consn eloci in he horizonl direcion nd consn ccelerion in he ericl
More informationHOMEWORK 6 - INTEGRATION. READING: Read the following parts from the Calculus Biographies that I have given (online supplement of our textbook):
MAT 3 CALCULUS I 5.. Dokuz Eylül Uiversiy Fculy of Sciece Deprme of Mhemics Isrucors: Egi Mermu d Cell Cem Srıoğlu HOMEWORK 6 - INTEGRATION web: hp://kisi.deu.edu.r/egi.mermu/ Tebook: Uiversiy Clculus,
More informationA 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 informationElectromechanical System Dynamics, energy Conversion, and Electromechanical Analogies. Modeling of Dynamic Systems
Elecroecicl Syse Dyics, eergy Coersio, d Elecroecicl Alogies Modelig of Dyic Syses Modelig of dyic syses y e doe i seerl wys: Use e sdrd equio of oio Newo s Lw for ecicl syses Use circuis eores O s lw
More informationMotion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.
Moion Accelerion Pr : Consn Accelerion Accelerion Accelerion Accelerion is he re of chnge of velociy. = v - vo = Δv Δ ccelerion = = v - vo chnge of velociy elpsed ime Accelerion is vecor, lhough in one-dimensionl
More informationAverage & 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 informationPhysic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = =
Mi i fd l Phsic 3 Lecure 4 Min poins of od s lecure: Emple: ddiion of elociies Trjecories of objecs in dimensions: dimensions: g 9.8m/s downwrds ( ) g o g g Emple: A foobll pler runs he pern gien in he
More information[ m] x = 0.25cos 20 t sin 20 t m
. x.si ( 5 s [ ] CHAPER OSCILLAIONS x ax (.( ( 5 6. s s ( ( ( xax. 5.7 s s. x.si [] x. cos s Whe, x a x.5. s 5s.6 s x. x( x cos + si a f ( ( [ ] x.5cos +.59si. ( ( cos α β cosαcos β + siαsi β x Acos φ
More informationIdeal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory
Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable
More information6.003: Signals and Systems Lecture 20 April 22, 2010
6.003: Sigals ad Sysems Lecure 0 April, 00 6.003: Sigals ad Sysems Relaios amog Fourier Represeaios Mid-erm Examiaio #3 Wedesday, April 8, 7:30-9:30pm. No reciaios o he day of he exam. Coverage: Lecures
More informationAn 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 informationS n. = n. Sum of first n terms of an A. P is
PROGREION I his secio we discuss hree impora series amely ) Arihmeic Progressio (A.P), ) Geomeric Progressio (G.P), ad 3) Harmoic Progressio (H.P) Which are very widely used i biological scieces ad humaiies.
More informationClass 36. Thin-film interference. Thin Film Interference. Thin Film Interference. Thin-film interference
Thi Film Ierferece Thi- ierferece Ierferece ewee ligh waves is he reaso ha hi s, such as soap ules, show colorful paers. Phoo credi: Mila Zikova, via Wikipedia Thi- ierferece This is kow as hi- ierferece
More informationA 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m
PHYS : Soluions o Chper 3 Home Work. SSM REASONING The displcemen is ecor drwn from he iniil posiion o he finl posiion. The mgniude of he displcemen is he shores disnce beween he posiions. Noe h i is onl
More informationExperiment 6: Fourier Series
Fourier Series Experime 6: Fourier Series Theory A Fourier series is ifiie sum of hrmoic fucios (sies d cosies) wih every erm i he series hvig frequecy which is iegrl muliple of some pricipl frequecy d
More informationUltrahigh Frequency Generation in GaAs-type. Two-Valley Semiconductors
Adv. Sudies Theo. Phys. Vol. 3 9 o. 8 93-98 lhigh Fequecy Geeio i GAs-ype Two-Vlley Seicoducos.. sov. K. Gsiov A. Z. Phov d A.. eiel Bu Se ivesiy 3 Z. Khlilov s. Az 48 Bu ciy- Physicl siue o he Azebij
More informationGraphing Review Part 3: Polynomials
Grphig Review Prt : Polomils Prbols Recll, tht the grph of f ( ) is prbol. It is eve fuctio, hece it is smmetric bout the bout the -is. This mes tht f ( ) f ( ). Its grph is show below. The poit ( 0,0)
More informationPure Math 30: Explained!
ure Mah : Explaied! www.puremah.com 6 Logarihms Lesso ar Basic Expoeial Applicaios Expoeial Growh & Decay: Siuaios followig his ype of chage ca be modeled usig he formula: (b) A = Fuure Amou A o = iial
More informationBINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k =
wwwskshieduciocom BINOMIAL HEOREM OBJEIVE PROBLEMS he coefficies of, i e esio of k e equl he k /7 If e coefficie of, d ems i e i AP, e e vlue of is he coefficies i e,, 7 ems i e esio of e i AP he 7 7 em
More informationIn an algebraic expression of the form (1), like terms are terms with the same power of the variables (in this case
Chpter : Algebr: A. Bckgroud lgebr: A. Like ters: I lgebric expressio of the for: () x b y c z x y o z d x... p x.. we cosider x, y, z to be vribles d, b, c, d,,, o,.. to be costts. I lgebric expressio
More informationVersion 001 test-1 swinney (57010) 1. is constant at m/s.
Version 001 es-1 swinne (57010) 1 This prin-ou should hve 20 quesions. Muliple-choice quesions m coninue on he nex column or pge find ll choices before nswering. CubeUniVec1x76 001 10.0 poins Acubeis1.4fee
More informationPhysics 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 informationONE RANDOM VARIABLE F ( ) [ ] x P X x x x 3
The Cumulive Disribuio Fucio (cd) ONE RANDOM VARIABLE cd is deied s he probbiliy o he eve { x}: F ( ) [ ] x P x x - Applies o discree s well s coiuous RV. Exmple: hree osses o coi x 8 3 x 8 8 F 3 3 7 x
More information1. Solve by the method of undetermined coefficients and by the method of variation of parameters. (4)
7 Differeial equaios Review Solve by he mehod of udeermied coefficies ad by he mehod of variaio of parameers (4) y y = si Soluio; we firs solve he homogeeous equaio (4) y y = 4 The correspodig characerisic
More informationExam 1: Tomorrow 8:20-10:10pm
x : Toorrow 8:0-0:0p Roo Assignents: Lst Ne Roo A-D CCC 00 -J CS A0 K- PUGH 70 N-Q LI 50 R-S RY 30 T-Z W 00 redown o the 0 Probles teril # o Probles Chpter 4 Chpter 3 Chpter 4 6 Chpter 5 3 Chpter 6 5 Crib
More informationModeling Driver Behavior as a Sequential Risk-Taking Task
Smer H. Hmdr Jury 15, 008 Deprme of Civil d Eviromel Egieerig Modelig Driver Behvior s Sequeil Risk-Tkig Tsk Smer H. Hmdr Mri Treiber Hi S. Mhmssi Are Kesig TRB Aul Meeig Wshigo DC 13-1717 Jury 008 Smer
More informationPHYSICS 211 MIDTERM I 21 April 2004
PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of
More informationProblems and Solutions for Section 3.2 (3.15 through 3.25)
3-7 Problems ad Soluios for Secio 3 35 hrough 35 35 Calculae he respose of a overdamped sigle-degree-of-freedom sysem o a arbirary o-periodic exciaio Soluio: From Equaio 3: x = # F! h "! d! For a overdamped
More informationCONTROL SYSTEMS. Chapter 3 : Time Response Analysis. [GATE EE 1991 IIT-Madras : 2 Mark]
CONTROL SYSTEMS Chper 3 : Time Repoe lyi GTE Objecive & Numericl Type Soluio Queio 4 [GTE EC 99 IIT-Mdr : Mrk] uiy feedbck corol yem h he ope loop rfer fucio. 4( ) G () ( ) If he ipu o he yem i ui rmp,
More informationMA123, Chapter 9: Computing some integrals (pp )
MA13, Chpter 9: Computig some itegrls (pp. 189-05) Dte: Chpter Gols: Uderstd how to use bsic summtio formuls to evlute more complex sums. Uderstd how to compute its of rtiol fuctios t ifiity. Uderstd how
More informationDepartment of Mathematical and Statistical Sciences University of Alberta
MATH 4 (R) Wier 008 Iermediae Calculus I Soluios o Problem Se # Due: Friday Jauary 8, 008 Deparme of Mahemaical ad Saisical Scieces Uiversiy of Albera Quesio. [Sec.., #] Fid a formula for he geeral erm
More informationPhysics 2A HW #3 Solutions
Chper 3 Focus on Conceps: 3, 4, 6, 9 Problems: 9, 9, 3, 41, 66, 7, 75, 77 Phsics A HW #3 Soluions Focus On Conceps 3-3 (c) The ccelerion due o grvi is he sme for boh blls, despie he fc h he hve differen
More informationPhysics 232 Exam II Mar. 28, 2005
Phi 3 M. 8, 5 So. Se # Ne. A piee o gl, ide o eio.5, h hi oig o oil o i. The oil h ide o eio.4.d hike o. Fo wh welegh, i he iile egio, do ou ge o eleio? The ol phe dieee i gie δ Tol δ PhDieee δ i,il δ
More informationwhen t = 2 s. Sketch the path for the first 2 seconds of motion and show the velocity and acceleration vectors for t = 2 s.(2/63)
. The -coordine of pricle in curiliner oion i gien b where i in eer nd i in econd. The -coponen of ccelerion in eer per econd ured i gien b =. If he pricle h -coponen = nd when = find he gniude of he eloci
More informationComparison between Fourier and Corrected Fourier Series Methods
Malaysia Joural of Mahemaical Scieces 7(): 73-8 (13) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Joural homepage: hp://eispem.upm.edu.my/oural Compariso bewee Fourier ad Correced Fourier Series Mehods 1
More informationSampling Example. ( ) δ ( f 1) (1/2)cos(12πt), T 0 = 1
Samplig Example Le x = cos( 4π)cos( π). The fudameal frequecy of cos 4π fudameal frequecy of cos π is Hz. The ( f ) = ( / ) δ ( f 7) + δ ( f + 7) / δ ( f ) + δ ( f + ). ( f ) = ( / 4) δ ( f 8) + δ ( f
More informationChapter 2 PROBLEM SOLUTIONS
Chper PROBLEM SOLUTIONS. We ssume h you re pproximely m ll nd h he nere impulse rels uniform speed. The elpsed ime is hen Δ x m Δ = m s s. s.3 Disnces reled beween pirs of ciies re ( ) Δx = Δ = 8. km h.5
More informationExtremal graph theory II: K t and K t,t
Exremal graph heory II: K ad K, Lecure Graph Theory 06 EPFL Frak de Zeeuw I his lecure, we geeralize he wo mai heorems from he las lecure, from riagles K 3 o complee graphs K, ad from squares K, o complee
More informationBig O Notation for Time Complexity of Algorithms
BRONX COMMUNITY COLLEGE of he Ciy Uiversiy of New York DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE CSI 33 Secio E01 Hadou 1 Fall 2014 Sepember 3, 2014 Big O Noaio for Time Complexiy of Algorihms Time
More informationChapter Direct Method of Interpolation
Chper 5. Direc Mehod of Inerpolion Afer reding his chper, you should be ble o:. pply he direc mehod of inerpolion,. sole problems using he direc mehod of inerpolion, nd. use he direc mehod inerpolns o
More informationElectrical Engineering Department Network Lab.
Par:- Elecrical Egieerig Deparme Nework Lab. Deermiaio of differe parameers of -por eworks ad verificaio of heir ierrelaio ships. Objecive: - To deermie Y, ad ABD parameers of sigle ad cascaded wo Por
More informationThe Spring. Consider a spring, which we apply a force F A to either stretch it or compress it
The Spring Consider spring, which we pply force F A to either stretch it or copress it F A - unstretched -F A 0 F A k k is the spring constnt, units of N/, different for different terils, nuber of coils
More informationSeptember 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 informationEGR 544 Communication Theory
EGR 544 Commuicaio heory 7. Represeaio of Digially Modulaed Sigals II Z. Aliyazicioglu Elecrical ad Compuer Egieerig Deparme Cal Poly Pomoa Represeaio of Digial Modulaio wih Memory Liear Digial Modulaio
More informationENGR 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 informationth m m m m central moment : E[( X X) ] ( X X) ( x X) f ( x)
1 Trasform Techiques h m m m m mome : E[ ] x f ( x) dx h m m m m ceral mome : E[( ) ] ( ) ( x) f ( x) dx A coveie wa of fidig he momes of a radom variable is he mome geeraig fucio (MGF). Oher rasform echiques
More informationLAWS OF INDICES M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier
Mthetics Revisio Guides Lws of Idices Pge of 7 Author: Mrk Kudlowski M.K. HOME TUITION Mthetics Revisio Guides Level: GCSE Higher Tier LAWS OF INDICES Versio:. Dte: 0--0 Mthetics Revisio Guides Lws of
More informationEedu : Pribh e/elerig This quesio pper ws prepred by seior fculy members of Sri Chiy Educiol siuios JEE-DVNCED MDEL GRND TEST PPER - Time : 3 hrs ] [Number of quesios : 6 PHYSCS SECTN Sigle Correc swer
More informationALGEBRA II CHAPTER 7 NOTES. Name
ALGEBRA II CHAPTER 7 NOTES Ne Algebr II 7. th Roots d Rtiol Expoets Tody I evlutig th roots of rel ubers usig both rdicl d rtiol expoet ottio. I successful tody whe I c evlute th roots. It is iportt for
More informationPhysics 2135 Exam 1 February 14, 2017
Exm Totl / 200 Physics 215 Exm 1 Ferury 14, 2017 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the est or most nerly correct nswer. 1. Two chrges 1 nd 2 re seprted
More informationBy Tom Irvine December 27,
THE STEADY-STATE VIBRATION RESPONSE OF A BAFFED PATE SIMPY-SUPPORTED ON A SIDES SUBJECTED TO RANDOM PRESSURE PANE WAVE EXCITATION AT OBIQUE INCIDENCE Revisi A By T Irvie Deceber 7, 04 Eil: @vibrid.c The
More informationP 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 information3 Motion with constant acceleration: Linear and projectile motion
3 Moion wih consn ccelerion: Liner nd projecile moion cons, In he precedin Lecure we he considered moion wih consn ccelerion lon he is: Noe h,, cn be posiie nd neie h leds o rie of behiors. Clerl similr
More information2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i)
Mah PracTes Be sure o review Lab (ad all labs) There are los of good quesios o i a) Sae he Mea Value Theorem ad draw a graph ha illusraes b) Name a impora heorem where he Mea Value Theorem was used i he
More informationThe Eigen Function of Linear Systems
1/25/211 The Eige Fucio of Liear Sysems.doc 1/7 The Eige Fucio of Liear Sysems Recall ha ha we ca express (expad) a ime-limied sigal wih a weighed summaio of basis fucios: v ( ) a ψ ( ) = where v ( ) =
More informationME 501A Seminar in Engineering Analysis Page 1
Seod ad igher Order Liear Differeial Equaios Oober 9, 7 Seod ad igher Order Liear Differeial Equaios Larr areo Mehaial Egieerig 5 Seiar i Egieerig alsis Oober 9, 7 Oulie Reiew las lass ad hoewor ppl aerial
More informationCHAPTER 2 KINEMATICS IN ONE DIMENSION ANSWERS TO FOCUS ON CONCEPTS QUESTIONS
Physics h Ediion Cunell Johnson Young Sdler Soluions Mnul Soluions Mnul, Answer keys, Insrucor's Resource Mnul for ll chpers re included. Compleed downlod links: hps://esbnkre.com/downlod/physics-h-ediion-soluions-mnulcunell-johnson-young-sdler/
More informationMagnetostatics 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 informationL-functions and Class Numbers
L-fucios ad Class Numbers Sude Number Theory Semiar S. M.-C. 4 Sepember 05 We follow Romyar Sharifi s Noes o Iwasawa Theory, wih some help from Neukirch s Algebraic Number Theory. L-fucios of Dirichle
More informationMoment Generating Function
1 Mome Geeraig Fucio m h mome m m m E[ ] x f ( x) dx m h ceral mome m m m E[( ) ] ( ) ( x ) f ( x) dx Mome Geeraig Fucio For a real, M () E[ e ] e k x k e p ( x ) discree x k e f ( x) dx coiuous Example
More informationThe sphere of radius a has the geographical form. r (,)=(acoscos,acossin,asin) T =(p(u)cos v, p(u)sin v,q(u) ) T.
Che 5. Dieeil Geome o Sces 5. Sce i meic om I 3D sce c be eeseed b. Elici om z =. Imlici om z = 3. Veco om = o moe geel =z deedig o wo mees. Emle. he shee o dis hs he geoghicl om =coscoscossisi Emle. he
More informationPhysics 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 informationECE-314 Fall 2012 Review Questions
ECE-34 Fall 0 Review Quesios. A liear ime-ivaria sysem has he ipu-oupu characerisics show i he firs row of he diagram below. Deermie he oupu for he ipu show o he secod row of he diagram. Jusify your aswer.
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/4 UNIT (COMMON) Time allowed Two hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 999 MATHEMATICS 3 UNIT (ADDITIONAL) AND 3/ UNIT (COMMON) Time llowed Two hours (Plus 5 miutes redig time) DIRECTIONS TO CANDIDATES Attempt ALL questios. ALL questios
More informationThe Change of the Distances between the Wave Fronts
Joural of Physical Mahemaics IN: 9-9 Research Aricle Aricle Joural of Physical Mahemaics Geadiy ad iali, J Phys Mah 7, 8: DOI: 47/9-97 OMI Ope Ieraioal Access Opical Fizeau Experime wih Movig Waer is Explaied
More information4. When is the particle speeding up? Why? 5. When is the particle slowing down? Why?
AB CALCULUS: 5.3 Positio vs Distce Velocity vs. Speed Accelertio All the questios which follow refer to the grph t the right.. Whe is the prticle movig t costt speed?. Whe is the prticle movig to the right?
More informationExponents 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 information4.8 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 informationP 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 informationEE757 Numerical Techniques in Electromagnetics Lecture 9
EE757 uericl Techiques i Elecroeics Lecure 9 EE757 06 Dr. Mohed Bkr Diereil Equios Vs. Ierl Equios Ierl equios ke severl ors e.. b K d b K d Mos diereil equios c be epressed s ierl equios e.. b F d d /
More information( ) k ( ) 1 T n 1 x = xk. Geometric series obtained directly from the definition. = 1 1 x. See also Scalars 9.1 ADV-1: lim n.
Sclrs-9.0-ADV- Algebric Tricks d Where Tylor Polyomils Come From 207.04.07 A.docx Pge of Algebric tricks ivolvig x. You c use lgebric tricks to simplify workig with the Tylor polyomils of certi fuctios..
More informationODEs II, Supplement to Lectures 6 & 7: The Jordan Normal Form: Solving Autonomous, Homogeneous Linear Systems. April 2, 2003
ODEs II, Suppleme o Lecures 6 & 7: The Jorda Normal Form: Solvig Auoomous, Homogeeous Liear Sysems April 2, 23 I his oe, we describe he Jorda ormal form of a marix ad use i o solve a geeral homogeeous
More informationManipulations involving the signal amplitude (dependent variable).
Oulie Maipulaio of discree ime sigals: Maipulaios ivolvig he idepede variable : Shifed i ime Operaios. Foldig, reflecio or ime reversal. Time Scalig. Maipulaios ivolvig he sigal ampliude (depede variable).
More informationThings I Should Know In Calculus Class
Thigs I Should Kow I Clculus Clss Qudrtic Formul = 4 ± c Pythgore Idetities si cos t sec cot csc + = + = + = Agle sum d differece formuls ( ) ( ) si ± y = si cos y± cos si y cos ± y = cos cos ym si si
More informationReview for the Midterm Exam.
Review for he iderm Exm Rememer! Gross re e re Vriles suh s,, /, p / p, r, d R re gross res 2 You should kow he disiio ewee he fesile se d he udge se, d kow how o derive hem The Fesile Se Wihou goverme
More informationB. Maddah INDE 504 Simulation 09/02/17
B. Maddah INDE 54 Simulaio 9/2/7 Queueig Primer Wha is a queueig sysem? A queueig sysem cosiss of servers (resources) ha provide service o cusomers (eiies). A Cusomer requesig service will sar service
More informationExercise 3 Stochastic Models of Manufacturing Systems 4T400, 6 May
Exercise 3 Sochasic Models of Maufacurig Sysems 4T4, 6 May. Each week a very popular loery i Adorra pris 4 ickes. Each ickes has wo 4-digi umbers o i, oe visible ad he oher covered. The umbers are radomly
More informationSUTCLIFFE S NOTES: CALCULUS 2 SWOKOWSKI S CHAPTER 11
UTCLIFFE NOTE: CALCULU WOKOWKI CHAPTER Ifiite eries Coverget or Diverget eries Cosider the sequece If we form the ifiite sum 0, 00, 000, 0 00 000, we hve wht is clled ifiite series We wt to fid the sum
More informationLet s express the absorption of radiation by dipoles as a dipole correlation function.
MIT Deparme of Chemisry 5.74, Sprig 004: Iroducory Quaum Mechaics II Isrucor: Prof. Adrei Tokmakoff p. 81 Time-Correlaio Fucio Descripio of Absorpio Lieshape Le s express he absorpio of radiaio by dipoles
More informationUCSD Phys 4A Intro Mechanics Winter 2016 Ch 4 Solutions
USD Phys 4 Intro Mechnics Winter 06 h 4 Solutions 0. () he 0.0 k box restin on the tble hs the free-body dir shown. Its weiht 0.0 k 9.80 s 96 N. Since the box is t rest, the net force on is the box ust
More informationRESPONSE OF A RECTANGULAR PLATE TO BASE EXCITATION Revision E W( )
RESPONSE OF A RECTANGULAR PLATE TO BASE EXCITATION Revisio E B To Ivie Eil: o@viiod.co Apil, 3 Viles A pliude coefficie E k leg id ple siffess fco elsic odulus ple ickess veue ple ss edig oe,, u, v ode
More informationUsing hypothesis one, energy of gravitational waves is directly proportional to its frequency,
ushl nd Grviy Prshn Shool of Siene nd ngineering, Universiy of Glsgow, Glsgow-G18QQ, Unied ingdo. * orresponding uhor: : Prshn. Shool of Siene nd ngineering, Universiy of Glsgow, Glsgow-G18QQ, Unied ingdo,
More information