Chapter 15 Oscillatory Motion I
|
|
- Kelley Gardner
- 5 years ago
- Views:
Transcription
1 Chaper 15 Oscillaory Moion I Level : AP Physics Insrucor : Kim Inroducion A very special kind of moion occurs when he force acing on a body is proporional o he displacemen of he body from some equilibrium posiion. If his force is always direced oward he equilibrium posiion, repeiive back-and-force moion occurs abou his posiion. Such moion is called periodic moion, or harmonic moion, oscillaion or vibraion. Eamples of periodic moion; a block aached o a spring, he swinging of a child on a playground, he moion of a pendulum, and he vibraions of a sringed musical insrumen, ec... The ideal moion is called simple harmonic moion, where here is no loss in energy Ideal Spring When he block is displaced a small disance from equilibrium, he spring eers on he block a force ha is proporional o he displacemen and given by Hook s law F s = k : Hook s Law We call his a resoring force because i is always direced oward he equilibrium posiion herefore opposie he displacemen. Tha is, if a force is applied o a spring, he spring eers an resoring force ha is always opposie in direcion F = F s + F app = 0 => F app = -F s => F app = -(-k) F app =k F app=k Q1) An objec of mass 9kg is hung on a spring, causing he spring o srech by =0.0191m. Then deermine he force needed o srech he spring by m. Fs Fapp a) 194N b) 235N c) 276N d) 310N (a) Fg =mg (b) Q2) The graph shows he force F ha an archer applies o he spring of a long bow versus he sring s displacemen. Drawing back his bow is analogous o sreching a spring. From he daa in he graph deermine he effecive spring consan of he bow a) 324.5N b) 397.1N c) 533.6N d) 666.7N F(N)
2 Simple Harmonic Moion and Posiion(or displacemen) Funcion over ime When a block of mass m is aached o a spring ha is FP neiher sreched nor compressed, he block is a he posiion =0, called he equilibrium posiion of he sysem. If he block is disurbed from is equilibrium posiion, he block will oscillae back and forh. =0 For eample, assuming he surface is fricionless, if he block is given a 'insananeous' push(f P) o he righ, hen he block will oscillae. If we record he posiion of he block hrough ime and plo in on a - graph, we can see he following; v=0 Fs (s) =0 =1m -1 Assume he block momenarily sops a posiion =1m and he ime i akes o reach ha posiion is =1.57s vma Fs= (s) =0-1 The block reurns o he origin, reaching maimum speed he momen i passes he origin v=0 Fs (s) = 1m =0-1 If he surface is fricionless, hen he block will be compressed unil i reaches = 1m. (maimum compression) vma Fs= (s) =0-1
3 Q4) A block is aached o spring and se in simple harmonic moion. Surface is fricionless. Which of he following funcion bes describes he posiion() funcion of he block as a funcion of ime? a) () = 2 b) () = 2 (c) () = 3 d) () = sin =0 ma Hence, he displacemen funcion ha bes describes he moion over ime can be epressed as () = sin where he maimum srech or compression is = ±1m. If he block is sreched or compressed more, like =2m, hen () = 2sin However, since our observaion begins according o our choice and if we happened o sar observing when he block is a he maimum srech from he equilibrium posiion, hen he displacemen funcion can be epressed as () = 2sin( + π ), where π/2=1.57 or () = 2cos 2 Hence, choosing cosine or sine funcion depends on when we sar our observaion =0 ma Q5) Which of he following funcion is equal o () = cos( - π)? There are wo answers a) () = sin b) () = sin( - π ) c) () = cos( - π ) d) () = cos e) () = cos 2 2 Q6) Which graph represens he posiion () funcion? Connec by drawing a line () = cos(+3π/2) () = cos(+π/2) () = cos( - π)
4 Newon's 2nd law and Posiion Funcion for Simple Harmonic Moion Applying Newon s 2 nd law o he moion of he block, we obain solving he above equaion gives F s = k= ma a = k m d 2 d 2 = k m ()=Acos(w+φ) where w 2 =k/m, k is he spring consan, m is mass of he block ()=Acos(w+φ) is he displacemen funcion of a paricle ehibiing simple harmonic moion. Tha is, he funcion provides he posiion of he paricle from he equilibrium a any ime - A is he ampliude, which represens he maimum displacemen of he paricle eiher he posiive or negaive direcion. - w is he angular frequency of he moion and has unis of rads /s - The consan angle φ is he phase consan. I is deermined by iniial displacemen and velociy of he paricle The quaniy (w + π) is called he phase of he moion and is useful in comparing he moion of wo oscillaors. Noe ha he rigonomeric funcion Acos(w+φ) is periodic and repeas iself every ime w increases by 2πrads. Here we can define he period T, since period T of he moion is he ime i akes for he paricle o go hrough one full cycle or one oscillaion. Hence, he value of a ime equals he value of a ime +T. Hence T = 2π w w + φ + 2π = w( +T) + φ In roaional moion, recall ha he angular speed w was defined as w=δθ/δ. If an objec complees one cycle, hen Δθ=2π and Δ=T. So w=δθ/δ=2π/t, hen angular speed, which is also ofen called angular frequency can be wrien as w = 2π T
5 The inverse of he period is called he frequency f of he moion. The frequency represens he number of oscillaions ha he paricle makes per uni ime: f = 1 T = w 2π and w = 2πf The uni of f are cycles per second, ha is s -1 or herz(hz). Since w= k m, he period can also be epressed as T=2π m k and f = 1 2π k m Summary F s= k and F app=k The posiion of a simple harmonic moion: ()=Acos(w+φ) A is he ampliude, w is he angular frequency where w= k, φ is he phase consan m T is he period where T = 2π w =2π m k f is he frequency where f = 1 T = w 2π = 1 2π k m Q7) An objec undergoes simple harmonic moion of ampliude A. Through wha oal disance does he objec move during one complee cycle of is moion? (a) A/2 (b) A (c) 2A (d) 4A Q8) If an objec akes 2seconds o complee one cycle, wha are he period, frequency and angular frequency? Check your answer below Ans) 2s, 0.5Hz, 3.14rad/s Velociy and Acceleraion Funcion for Simple Harmonic Moion We can obain he linear velociy of a paricle undergoing simple harmonic moion by differeniaing equaion ()=Acos(w+φ) The speed of he paricle is v()= d = -wasin(w + φ ), where vma=wa (compare wih v=rw) d The acceleraion of he paricle is a() = dv d = -w2 Acos(w + φ ), where a ma=w 2 A(compare wih a r=v 2 /r=w 2 r)
6 Displacemen vs Velociy vs Acceleraion A block aached o a spring on a fricionless surface is pulled a cerain disance away from he equilibrium and hen released. The block has maimum displacemen he insan i was released. A ha momen, he speed is minimum and acceleraion is maimum. (a) Displacemen vs ime graph is shown. () is maimum he momen he block is being released. () is minimum he momen he block passes he equilibrium posiion ()=Acos(w) (b) Velociy vs ime graph is shown. v()=0 he momen he block is being released. v() is maimum in he negaive direcion he momen he block passes he equilibrium posiion () A -A v() wa v()= d d = -Awsin(w) (c) Acceleraion vs ime graph is shown. a() is maimum in negaive direcion he momen he block is being released. a()=0 he momen he block passes he equilibrium posiion a()= dv d = -Aw2 cos(w) -wa -w 2 A a() w 2 A Calculaors mus be in radians!!!!!! Or plunge ino forever darkness~ Q9) The displacemen of a paricle a =0.25s is given by he epression ()=(4.00m)cos(3π + π), where is in meers and is in seconds. Deermine meers (a) he frequency and period of he moion Ans) 1.5Hz, 0.67s (b) he ampliude of he moion (c) he phase consan Ans) 4m Ans) π (d) he displacemen of he paricle a =0.25s. Ans) 2.83m (e) Plo a displacemen vs ime graph of he moion below. Plo your graph manually and hen check calculaor (s)
7 Q10) An objec oscillaes wih simple harmonic moion along he ais. Is displacemen from he origin varies wih ime according o he equaion = (4.00m) cos( π + π 4 ) where is in seconds and he angles in he parenheses are in radians. (a) Deermine he ampliude, frequency and period of he moion Ans) 4m, 0.5Hz, 2s (b) Calculae he speed and acceleraion of he objec a ime =1s. Ans) 8.89m/s (righ) 27.9m/s 2 (c) Deermine he maimum speed and a wha ime does he objec have maimum speed? Ans) 12.6m/s, v ma a = 0.25s, 1.25s, 2.25s,.... (d) Plo a displacemen vs ime graph of he moion below. (s) (e) Find he displacemen of he objec beween = 0 and =1s and he disance raveled during hose ime. Ans) = 5.66m, d=8m
8 Q11) A 0.8kg objec is aached o one end of a spring and he sysem is se ino simple harmonic moion. The displacemen of he objec as a funcion of ime is shown. Wih he aid of his daa, deermine he (a) ampliude A of he moion Ans) 0.08m (b) he angular frequency w and frequency f ime(s) Ans) 1.57rad/s, 0.25Hz (c) he spring consan k Ans)1.97N/m (d) he maimum displacemen from he equilibrium posiion ma Ans) 0.08m (e) A wha ime(s) is he objec a he equilibrium posiion? Ans) =0,2,4,.. (f) Epress he displacemen of he moion as a funcion of ime () Ans) ()=0.08cos( π 2 π 2 ) or 0.08sin( π 2 ) (g) Find he posiion of he objec a =0.2, 0.5, 2.4, 3.0 seconds Ans) m, m, 0.047m, 0.08m (h) Wha is he maimum speed of he objec? Also find he epression for speed as a funcion of ime v() Ans) m/s, v()= 0.04πsin( π 2 π 2 ) (i) Find he speed of he objec a =0.4, 1.5 and 3.2 seconds. Ans) 0.102m/s, 0.089m/s, 0.039m/s (j) Find he an epression for acceleraion as a funcion of ime a() and find he acceleraion a =0.4, 1.5, 3.2, 3.9, 3.99, seconds Ans) a()= 0.02π 2 cos( π 2 π 2 ), 0.116m/s2, 0.14m/s 2, 0.188m/s 2, m/s 2, m/s 2, approach 0
Section 3.8, Mechanical and Electrical Vibrations
Secion 3.8, Mechanical and Elecrical Vibraions Mechanical Unis in he U.S. Cusomary and Meric Sysems Disance Mass Time Force g (Earh) Uni U.S. Cusomary MKS Sysem CGS Sysem fee f slugs seconds sec pounds
More informationSome Basic Information about M-S-D Systems
Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,
More informationA. Using Newton s second law in one dimension, F net. , write down the differential equation that governs the motion of the block.
Simple SIMPLE harmonic HARMONIC moion MOTION I. Differenial equaion of moion A block is conneced o a spring, one end of which is aached o a wall. (Neglec he mass of he spring, and assume he surface is
More informationOscillations. Periodic Motion. Sinusoidal Motion. PHY oscillations - J. Hedberg
Oscillaions PHY 207 - oscillaions - J. Hedberg - 2017 1. Periodic Moion 2. Sinusoidal Moion 3. How do we ge his kind of moion? 4. Posiion - Velociy - cceleraion 5. spring wih vecors 6. he reference circle
More informationChapter 2. Motion in One-Dimension I
Chaper 2. Moion in One-Dimension I Level : AP Physics Insrucor : Kim 1. Average Rae of Change and Insananeous Velociy To find he average velociy(v ) of a paricle, we need o find he paricle s displacemen
More information2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance
Ch: Moion along a sraigh line Moion Posiion and Displacemen Average Velociy and Average Speed Insananeous Velociy and Speed Acceleraion Consan Acceleraion: A Special Case Anoher Look a Consan Acceleraion
More informationMEI Mechanics 1 General motion. Section 1: Using calculus
Soluions o Exercise MEI Mechanics General moion Secion : Using calculus. s 4 v a 6 4 4 When =, v 4 a 6 4 6. (i) When = 0, s = -, so he iniial displacemen = - m. s v 4 When = 0, v = so he iniial velociy
More informationChapters 6 & 7: Trigonometric Functions of Angles and Real Numbers. Divide both Sides by 180
Algebra Chapers & : Trigonomeric Funcions of Angles and Real Numbers Chapers & : Trigonomeric Funcions of Angles and Real Numbers - Angle Measures Radians: - a uni (rad o measure he size of an angle. rad
More informationAP Calculus BC Chapter 10 Part 1 AP Exam Problems
AP Calculus BC Chaper Par AP Eam Problems All problems are NO CALCULATOR unless oherwise indicaed Parameric Curves and Derivaives In he y plane, he graph of he parameric equaions = 5 + and y= for, is a
More informationPhysics 20 Lesson 5 Graphical Analysis Acceleration
Physics 2 Lesson 5 Graphical Analysis Acceleraion I. Insananeous Velociy From our previous work wih consan speed and consan velociy, we know ha he slope of a posiion-ime graph is equal o he velociy of
More informationWeek 1 Lecture 2 Problems 2, 5. What if something oscillates with no obvious spring? What is ω? (problem set problem)
Week 1 Lecure Problems, 5 Wha if somehing oscillaes wih no obvious spring? Wha is ω? (problem se problem) Sar wih Try and ge o SHM form E. Full beer can in lake, oscillaing F = m & = ge rearrange: F =
More informationTraveling Waves. Chapter Introduction
Chaper 4 Traveling Waves 4.1 Inroducion To dae, we have considered oscillaions, i.e., periodic, ofen harmonic, variaions of a physical characerisic of a sysem. The sysem a one ime is indisinguishable from
More informationChapter 11 VIBRATORY MOTION
Ch. 11--Vibraory Moion Chaper 11 VIBRATORY MOTION Noe: There are wo areas of ineres when discussing oscillaory moion: he mahemaical characerizaion of vibraing srucures ha generae waves and he ineracion
More informationParametrics and Vectors (BC Only)
Paramerics and Vecors (BC Only) The following relaionships should be learned and memorized. The paricle s posiion vecor is r() x(), y(). The velociy vecor is v(),. The speed is he magniude of he velociy
More informationIn a shop window an illuminated spot on a display oscillates between positions W and Z with simple harmonic motion.
Quesions 1 and 2 refer o he informaion below. In a shop window an illuminaed spo on a display oscillaes beween posiions W and Z wih simple harmonic moion. The diagram shows he display wih a scale added.
More informationPhys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole
Phys 221 Fall 2014 Chaper 2 Moion in One Dimension 2014, 2005 A. Dzyubenko 2004 Brooks/Cole 1 Kinemaics Kinemaics, a par of classical mechanics: Describes moion in erms of space and ime Ignores he agen
More informationWall. x(t) f(t) x(t = 0) = x 0, t=0. which describes the motion of the mass in absence of any external forcing.
MECHANICS APPLICATIONS OF SECOND-ORDER ODES 7 Mechanics applicaions of second-order ODEs Second-order linear ODEs wih consan coefficiens arise in many physical applicaions. One physical sysems whose behaviour
More information4.5 Constant Acceleration
4.5 Consan Acceleraion v() v() = v 0 + a a() a a() = a v 0 Area = a (a) (b) Figure 4.8 Consan acceleraion: (a) velociy, (b) acceleraion When he x -componen of he velociy is a linear funcion (Figure 4.8(a)),
More information1. VELOCITY AND ACCELERATION
1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under
More informationKINEMATICS IN ONE DIMENSION
KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec
More informationLecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.
Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in
More informationSection 7.4 Modeling Changing Amplitude and Midline
488 Chaper 7 Secion 7.4 Modeling Changing Ampliude and Midline While sinusoidal funcions can model a variey of behaviors, i is ofen necessary o combine sinusoidal funcions wih linear and exponenial curves
More informationChapter Q1. We need to understand Classical wave first. 3/28/2004 H133 Spring
Chaper Q1 Inroducion o Quanum Mechanics End of 19 h Cenury only a few loose ends o wrap up. Led o Relaiviy which you learned abou las quarer Led o Quanum Mechanics (1920 s-30 s and beyond) Behavior of
More informationDisplacement ( x) x x x
Kinemaics Kinemaics is he branch of mechanics ha describes he moion of objecs wihou necessarily discussing wha causes he moion. 1-Dimensional Kinemaics (or 1- Dimensional moion) refers o moion in a sraigh
More informationPhysics 221 Fall 2008 Homework #2 Solutions Ch. 2 Due Tues, Sept 9, 2008
Physics 221 Fall 28 Homework #2 Soluions Ch. 2 Due Tues, Sep 9, 28 2.1 A paricle moving along he x-axis moves direcly from posiion x =. m a ime =. s o posiion x = 1. m by ime = 1. s, and hen moves direcly
More informationGround Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan
Ground Rules PC11 Fundamenals of Physics I Lecures 3 and 4 Moion in One Dimension A/Prof Tay Seng Chuan 1 Swich off your handphone and pager Swich off your lapop compuer and keep i No alking while lecure
More informationWelcome Back to Physics 215!
Welcome Back o Physics 215! (General Physics I) Thurs. Jan 19 h, 2017 Lecure01-2 1 Las ime: Syllabus Unis and dimensional analysis Today: Displacemen, velociy, acceleraion graphs Nex ime: More acceleraion
More informationSpeed and Velocity. Overview. Velocity & Speed. Speed & Velocity. Instantaneous Velocity. Instantaneous and Average
Overview Kinemaics: Descripion of Moion Posiion and displacemen velociy»insananeous acceleraion»insananeous Speed Velociy Speed and Velociy Speed & Velociy Velociy & Speed A physics eacher walks 4 meers
More informationThus the force is proportional but opposite to the displacement away from equilibrium.
Chaper 3 : Siple Haronic Moion Hooe s law saes ha he force (F) eered by an ideal spring is proporional o is elongaion l F= l where is he spring consan. Consider a ass hanging on a he spring. In equilibriu
More informationIB Physics Kinematics Worksheet
IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?
More informationExam I. Name. Answer: a. W B > W A if the volume of the ice cubes is greater than the volume of the water.
Name Exam I 1) A hole is punched in a full milk caron, 10 cm below he op. Wha is he iniial veloci of ouflow? a. 1.4 m/s b. 2.0 m/s c. 2.8 m/s d. 3.9 m/s e. 2.8 m/s Answer: a 2) In a wind unnel he pressure
More informationLAB 6: SIMPLE HARMONIC MOTION
1 Name Dae Day/Time of Lab Parner(s) Lab TA Objecives LAB 6: SIMPLE HARMONIC MOTION To undersand oscillaion in relaion o equilibrium of conservaive forces To manipulae he independen variables of oscillaion:
More informationSolution: b All the terms must have the dimension of acceleration. We see that, indeed, each term has the units of acceleration
PHYS 54 Tes Pracice Soluions Spring 8 Q: [4] Knowing ha in he ne epression a is acceleraion, v is speed, is posiion and is ime, from a dimensional v poin of view, he equaion a is a) incorrec b) correc
More informationPhysics for Scientists and Engineers I
Physics for Scieniss and Engineers I PHY 48, Secion 4 Dr. Beariz Roldán Cuenya Universiy of Cenral Florida, Physics Deparmen, Orlando, FL Chaper - Inroducion I. General II. Inernaional Sysem of Unis III.
More information1. Kinematics I: Position and Velocity
1. Kinemaics I: Posiion and Velociy Inroducion The purpose of his eperimen is o undersand and describe moion. We describe he moion of an objec by specifying is posiion, velociy, and acceleraion. In his
More informationLecture 23 Damped Motion
Differenial Equaions (MTH40) Lecure Daped Moion In he previous lecure, we discussed he free haronic oion ha assues no rearding forces acing on he oving ass. However No rearding forces acing on he oving
More information2001 November 15 Exam III Physics 191
1 November 15 Eam III Physics 191 Physical Consans: Earh s free-fall acceleraion = g = 9.8 m/s 2 Circle he leer of he single bes answer. quesion is worh 1 poin Each 3. Four differen objecs wih masses:
More informationLab #2: Kinematics in 1-Dimension
Reading Assignmen: Chaper 2, Secions 2-1 hrough 2-8 Lab #2: Kinemaics in 1-Dimension Inroducion: The sudy of moion is broken ino wo main areas of sudy kinemaics and dynamics. Kinemaics is he descripion
More informationTwo Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
More informationSuggested Practice Problems (set #2) for the Physics Placement Test
Deparmen of Physics College of Ars and Sciences American Universiy of Sharjah (AUS) Fall 014 Suggesed Pracice Problems (se #) for he Physics Placemen Tes This documen conains 5 suggesed problems ha are
More informationConstant Acceleration
Objecive Consan Acceleraion To deermine he acceleraion of objecs moving along a sraigh line wih consan acceleraion. Inroducion The posiion y of a paricle moving along a sraigh line wih a consan acceleraion
More informationSPH3U1 Lesson 03 Kinematics
SPH3U1 Lesson 03 Kinemaics GRAPHICAL ANALYSIS LEARNING GOALS Sudens will Learn how o read values, find slopes and calculae areas on graphs. Learn wha hese values mean on boh posiion-ime and velociy-ime
More informationWave Motion Sections 1,2,4,5, I. Outlook II. What is wave? III.Kinematics & Examples IV. Equation of motion Wave equations V.
Secions 1,,4,5, I. Oulook II. Wha is wave? III.Kinemaics & Eamples IV. Equaion of moion Wave equaions V. Eamples Oulook Translaional and Roaional Moions wih Several phsics quaniies Energ (E) Momenum (p)
More informationPHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections
PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.2-2.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx
More informationOscillations 15-1 SIMPLE HARMONIC MOTION. Learning Objectives After reading this module, you should be able to...
C H A P T E R 5 Oscillaions 5- SIMPLE HARMONIC MOTION Learning Objecives Afer reading his module, you should be able o... 5.0 Disinguish simple harmonic moion from oher ypes of periodic moion. 5.0 For
More informationKinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8.
Kinemaics Vocabulary Kinemaics and One Dimensional Moion 8.1 WD1 Kinema means movemen Mahemaical descripion of moion Posiion Time Inerval Displacemen Velociy; absolue value: speed Acceleraion Averages
More informationLINEAR MODELS: INITIAL-VALUE PROBLEMS
5 LINEAR MODELS: INITIAL-VALUE PROBLEMS 9 5 LINEAR MODELS: INITIAL-VALUE PROBLEMS REVIEW MATERIAL Secions 4, 4, and 44 Problems 9 6 in Eercises 4 Problems 7 6 in Eercises 44 INTRODUCTION In his secion
More informationk 1 k 2 x (1) x 2 = k 1 x 1 = k 2 k 1 +k 2 x (2) x k series x (3) k 2 x 2 = k 1 k 2 = k 1+k 2 = 1 k k 2 k series
Final Review A Puzzle... Consider wo massless springs wih spring consans k 1 and k and he same equilibrium lengh. 1. If hese springs ac on a mass m in parallel, hey would be equivalen o a single spring
More informationModule 3: The Damped Oscillator-II Lecture 3: The Damped Oscillator-II
Module 3: The Damped Oscillaor-II Lecure 3: The Damped Oscillaor-II 3. Over-damped Oscillaions. This refers o he siuaion where β > ω (3.) The wo roos are and α = β + α 2 = β β 2 ω 2 = (3.2) β 2 ω 2 = 2
More informationPHYSICS 149: Lecture 9
PHYSICS 149: Lecure 9 Chaper 3 3.2 Velociy and Acceleraion 3.3 Newon s Second Law of Moion 3.4 Applying Newon s Second Law 3.5 Relaive Velociy Lecure 9 Purdue Universiy, Physics 149 1 Velociy (m/s) The
More information15. Vector Valued Functions
1. Vecor Valued Funcions Up o his poin, we have presened vecors wih consan componens, for example, 1, and,,4. However, we can allow he componens of a vecor o be funcions of a common variable. For example,
More informationOf all of the intellectual hurdles which the human mind has confronted and has overcome in the last fifteen hundred years, the one which seems to me
Of all of he inellecual hurdles which he human mind has confroned and has overcome in he las fifeen hundred years, he one which seems o me o have been he mos amazing in characer and he mos supendous in
More informationToday: Graphing. Note: I hope this joke will be funnier (or at least make you roll your eyes and say ugh ) after class. v (miles per hour ) Time
+v Today: Graphing v (miles per hour ) 9 8 7 6 5 4 - - Time Noe: I hope his joke will be funnier (or a leas make you roll your eyes and say ugh ) afer class. Do yourself a favor! Prof Sarah s fail-safe
More informationNEWTON S SECOND LAW OF MOTION
Course and Secion Dae Names NEWTON S SECOND LAW OF MOTION The acceleraion of an objec is defined as he rae of change of elociy. If he elociy changes by an amoun in a ime, hen he aerage acceleraion during
More informationKinematics Motion in 1 Dimension and Graphs
Kinemaics Moion in 1 Dimension and Graphs Lana Sheridan De Anza College Sep 27, 2017 Las ime moion in 1-dimension some kinemaic quaniies graphs Overview velociy and speed acceleraion more graphs Kinemaics
More informationx(m) t(sec ) Homework #2. Ph 231 Introductory Physics, Sp-03 Page 1 of 4
Homework #2. Ph 231 Inroducory Physics, Sp-03 Page 1 of 4 2-1A. A person walks 2 miles Eas (E) in 40 minues and hen back 1 mile Wes (W) in 20 minues. Wha are her average speed and average velociy (in ha
More informationAP CALCULUS AB 2003 SCORING GUIDELINES (Form B)
SCING GUIDELINES (Form B) Quesion 4 A paricle moves along he x-axis wih velociy a ime given by v( ) = 1 + e1. (a) Find he acceleraion of he paricle a ime =. (b) Is he speed of he paricle increasing a ime
More informationLab 10: RC, RL, and RLC Circuits
Lab 10: RC, RL, and RLC Circuis In his experimen, we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors. We will sudy he way volages and currens change in
More informationPhysics Notes - Ch. 2 Motion in One Dimension
Physics Noes - Ch. Moion in One Dimension I. The naure o physical quaniies: scalars and ecors A. Scalar quaniy ha describes only magniude (how much), NOT including direcion; e. mass, emperaure, ime, olume,
More informationStructural Dynamics and Earthquake Engineering
Srucural Dynamics and Earhquae Engineering Course 1 Inroducion. Single degree of freedom sysems: Equaions of moion, problem saemen, soluion mehods. Course noes are available for download a hp://www.c.up.ro/users/aurelsraan/
More information0 time. 2 Which graph represents the motion of a car that is travelling along a straight road with a uniformly increasing speed?
1 1 The graph relaes o he moion of a falling body. y Which is a correc descripion of he graph? y is disance and air resisance is negligible y is disance and air resisance is no negligible y is speed and
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationPhysics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs.
Physics 180A Fall 2008 Tes 1-120 poins Name Provide he bes answer o he following quesions and problems. Wach your sig figs. 1) The number of meaningful digis in a number is called he number of. When numbers
More informationMechanics Acceleration The Kinematics Equations
Mechanics Acceleraion The Kinemaics Equaions Lana Sheridan De Anza College Sep 27, 2018 Las ime kinemaic quaniies graphs of kinemaic quaniies Overview acceleraion he kinemaics equaions (consan acceleraion)
More information2002 November 14 Exam III Physics 191
November 4 Exam III Physics 9 Physical onsans: Earh s free-fall acceleraion = g = 9.8 m/s ircle he leer of he single bes answer. quesion is worh poin Each 3. Four differen objecs wih masses: m = kg, m
More informationA man pushes a 500 kg block along the x axis by a constant force. Find the power required to maintain a speed of 5.00 m/s.
Coordinaor: Dr. F. hiari Wednesday, July 16, 2014 Page: 1 Q1. The uniform solid block in Figure 1 has mass 0.172 kg and edge lenghs a = 3.5 cm, b = 8.4 cm, and c = 1.4 cm. Calculae is roaional ineria abou
More informationDynamics. Option topic: Dynamics
Dynamics 11 syllabusref Opion opic: Dynamics eferenceence In his cha chaper 11A Differeniaion and displacemen, velociy and acceleraion 11B Inerpreing graphs 11C Algebraic links beween displacemen, velociy
More informationWe may write the basic equation of motion for the particle, as
We ma wrie he basic equaion of moion for he paricle, as or F m dg F F linear impulse G dg G G G G change in linear F momenum dg The produc of force and ime is defined as he linear impulse of he force,
More informationMotion along a Straight Line
chaper 2 Moion along a Sraigh Line verage speed and average velociy (Secion 2.2) 1. Velociy versus speed Cone in he ebook: fer Eample 2. Insananeous velociy and insananeous acceleraion (Secions 2.3, 2.4)
More informationChapter 1 Rotational dynamics 1.1 Angular acceleration
Chaper Roaional dynamics. Angular acceleraion Learning objecives: Wha do we mean by angular acceleraion? How can we calculae he angular acceleraion of a roaing objec when i speeds up or slows down? How
More informationOne-Dimensional Kinematics
One-Dimensional Kinemaics One dimensional kinemaics refers o moion along a sraigh line. Een hough we lie in a 3-dimension world, moion can ofen be absraced o a single dimension. We can also describe moion
More informationWEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x
WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile
More information!!"#"$%&#'()!"#&'(*%)+,&',-)./0)1-*23)
"#"$%&#'()"#&'(*%)+,&',-)./)1-*) #$%&'()*+,&',-.%,/)*+,-&1*#$)()5*6$+$%*,7&*-'-&1*(,-&*6&,7.$%$+*&%'(*8$&',-,%'-&1*(,-&*6&,79*(&,%: ;..,*&1$&$.$%&'()*1$$.,'&',-9*(&,%)?%*,('&5
More information4.6 One Dimensional Kinematics and Integration
4.6 One Dimensional Kinemaics and Inegraion When he acceleraion a( of an objec is a non-consan funcion of ime, we would like o deermine he ime dependence of he posiion funcion x( and he x -componen of
More informationChapter 2. Motion along a straight line
Chaper Moion along a sraigh line Kinemaics & Dynamics Kinemaics: Descripion of Moion wihou regard o is cause. Dynamics: Sudy of principles ha relae moion o is cause. Basic physical ariables in kinemaics
More informationPhysics 3A: Basic Physics I Shoup Sample Midterm. Useful Equations. x f. x i v x. a x. x i. v xi v xf. 2a x f x i. y f. a r.
Physics 3A: Basic Physics I Shoup Sample Miderm Useful Equaions A y Asin A A x A y an A y A x A = A x i + A y j + A z k A * B = A B cos(θ) A x B = A B sin(θ) A * B = A x B x + A y B y + A z B z A x B =
More informationGravity and SHM Review Questions
Graviy an SHM Review Quesions 1. The mass of Plane X is one-enh ha of he Earh, an is iameer is one-half ha of he Earh. The acceleraion ue o raviy a he surface of Plane X is mos nearly m/s (B) 4m/s (C)
More informationDecimal moved after first digit = 4.6 x Decimal moves five places left SCIENTIFIC > POSITIONAL. a) g) 5.31 x b) 0.
PHYSICS 20 UNIT 1 SCIENCE MATH WORKSHEET NAME: A. Sandard Noaion Very large and very small numbers are easily wrien using scienific (or sandard) noaion, raher han decimal (or posiional) noaion. Sandard
More informationLinear Motion I Physics
Linear Moion I Physics Objecives Describe he ifference beween isplacemen an isance Unersan he relaionship beween isance, velociy, an ime Describe he ifference beween velociy an spee Be able o inerpre a
More informationx y θ = 31.8 = 48.0 N. a 3.00 m/s
4.5.IDENTIY: Vecor addiion. SET UP: Use a coordinae sse where he dog A. The forces are skeched in igure 4.5. EXECUTE: + -ais is in he direcion of, A he force applied b =+ 70 N, = 0 A B B A = cos60.0 =
More informationPhysics 101: Lecture 03 Kinematics Today s lecture will cover Textbook Sections (and some Ch. 4)
Physics 101: Lecure 03 Kinemaics Today s lecure will coer Texbook Secions 3.1-3.3 (and some Ch. 4) Physics 101: Lecure 3, Pg 1 A Refresher: Deermine he force exered by he hand o suspend he 45 kg mass as
More informationt A. 3. Which vector has the largest component in the y-direction, as defined by the axes to the right?
Ke Name Insrucor Phsics 1210 Exam 1 Sepember 26, 2013 Please wrie direcl on he exam and aach oher shees of work if necessar. Calculaors are allowed. No noes or books ma be used. Muliple-choice problems
More informationx i v x t a dx dt t x
Physics 3A: Basic Physics I Shoup - Miderm Useful Equaions A y A sin A A A y an A y A A = A i + A y j + A z k A * B = A B cos(θ) A B = A B sin(θ) A * B = A B + A y B y + A z B z A B = (A y B z A z B y
More informationUniversity Physics with Modern Physics 14th Edition Young TEST BANK
Universi Phsics wih Modern Phsics 14h Ediion Young SOLUTIONS MANUAL Full clear download (no formaing errors) a: hps://esbankreal.com/download/universi-phsics-modern-phsics- 14h-ediion-oung-soluions-manual-/
More information2. What is the displacement of the bug between t = 0.00 s and t = 20.0 s? A) cm B) 39.9 cm C) cm D) 16.1 cm E) +16.
1. For which one of he following siuaions will he pah lengh equal he magniude of he displacemen? A) A jogger is running around a circular pah. B) A ball is rolling down an inclined plane. C) A rain ravels
More informationLAB # 2 - Equilibrium (static)
AB # - Equilibrium (saic) Inroducion Isaac Newon's conribuion o physics was o recognize ha despie he seeming compleiy of he Unierse, he moion of is pars is guided by surprisingly simple aws. Newon's inspiraion
More informationLecture 4 Kinetics of a particle Part 3: Impulse and Momentum
MEE Engineering Mechanics II Lecure 4 Lecure 4 Kineics of a paricle Par 3: Impulse and Momenum Linear impulse and momenum Saring from he equaion of moion for a paricle of mass m which is subjeced o an
More informationPracticing Problem Solving and Graphing
Pracicing Problem Solving and Graphing Tes 1: Jan 30, 7pm, Ming Hsieh G20 The Bes Ways To Pracice for Tes Bes If need more, ry suggesed problems from each new opic: Suden Response Examples A pas opic ha
More informationIn this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should
Cambridge Universiy Press 978--36-60033-7 Cambridge Inernaional AS and A Level Mahemaics: Mechanics Coursebook Excerp More Informaion Chaper The moion of projeciles In his chaper he model of free moion
More informationSPH3U: Projectiles. Recorder: Manager: Speaker:
SPH3U: Projeciles Now i s ime o use our new skills o analyze he moion of a golf ball ha was ossed hrough he air. Le s find ou wha is special abou he moion of a projecile. Recorder: Manager: Speaker: 0
More informationAnswers to 1 Homework
Answers o Homework. x + and y x 5 y To eliminae he parameer, solve for x. Subsiue ino y s equaion o ge y x.. x and y, x y x To eliminae he parameer, solve for. Subsiue ino y s equaion o ge x y, x. (Noe:
More informationEquations of motion for constant acceleration
Lecure 3 Chaper 2 Physics I 01.29.2014 Equaions of moion for consan acceleraion Course websie: hp://faculy.uml.edu/andriy_danylo/teaching/physicsi Lecure Capure: hp://echo360.uml.edu/danylo2013/physics1spring.hml
More information3.6 Derivatives as Rates of Change
3.6 Derivaives as Raes of Change Problem 1 John is walking along a sraigh pah. His posiion a he ime >0 is given by s = f(). He sars a =0from his house (f(0) = 0) and he graph of f is given below. (a) Describe
More informationElectrical Circuits. 1. Circuit Laws. Tools Used in Lab 13 Series Circuits Damped Vibrations: Energy Van der Pol Circuit
V() R L C 513 Elecrical Circuis Tools Used in Lab 13 Series Circuis Damped Vibraions: Energy Van der Pol Circui A series circui wih an inducor, resisor, and capacior can be represened by Lq + Rq + 1, a
More informationPhysics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle
Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,
More information2.5. The equation of the spring
2.5. The equaion of he spring I moun a spring wih a weigh on i. I ie he op of he spring o a sick projecing ou he op end of a cupboard door, and fasen a ruler down he edge of he door, so ha as he spring
More informationHOMEWORK # 2: MATH 211, SPRING Note: This is the last solution set where I will describe the MATLAB I used to make my pictures.
HOMEWORK # 2: MATH 2, SPRING 25 TJ HITCHMAN Noe: This is he las soluion se where I will describe he MATLAB I used o make my picures.. Exercises from he ex.. Chaper 2.. Problem 6. We are o show ha y() =
More informationMEI STRUCTURED MATHEMATICS 4758
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Cerificae of Educaion Advanced General Cerificae of Educaion MEI STRUCTURED MATHEMATICS 4758 Differenial Equaions Thursday 5 JUNE 006 Afernoon
More informationMOMENTUM CONSERVATION LAW
1 AAST/AEDT AP PHYSICS B: Impulse and Momenum Le us run an experimen: The ball is moving wih a velociy of V o and a force of F is applied on i for he ime inerval of. As he resul he ball s velociy changes
More information