Physics 201 Lecture 29
|
|
- Stephen Richard
- 5 years ago
- Views:
Transcription
1 Phsics 1 ecture 9 Goals ecture 9 v Describe oscillator otion in a siple pendulu v Describe oscillator otion with torques v Introduce daping in SHM v Discuss resonance v Final Ea Details l Sunda, Ma 13th 1:5a-1:5p in 15 Ag Hall & quiet roo l Forat: v Closed boo v Up to 4 8½1 sheets, hand written onl v Approiatel 5% fro Chapters and 5% 1-1 v Bring a calculator l Special needs/ conflicts: All requests for alternative test arrangeents should be ade b hursda Ma1th (ecept for edical eergenc) Phsics 1: ecture 9, Pg 1 Phsics 1: ecture 9, Pg Mechanical Energ of the Spring-Mass Sste (t) = A cos( ωt + φ ) v(t) = -ωa sin( ωt + φ ) a(t) = -ω A cos( ωt + φ ) Kinetic energ is alwas K = ½ v = ½ (ωa) sin (ωt+φ) Potential energ of a spring is, U = ½ = ½ A cos (ωt + φ) And ω = / or = ω K + U = constant Phsics 1: ecture 9, Pg 3 SHM is a close as ae Mendota So can ou estiate the characteristic frequenc for a bobbing in the water? If ou have equilibriu and there is a linear restoring force, then es with ω = ( / ) ½ At equlibriu F = = F g F = g = ρ A g B w FB g B Phsics 1: ecture 9, Pg 4 SHM is a close as ae Mendota Deeper than eans B = ρ and a net force of F wag F = ρw A ) g A linear restoring force with = ρ w Ag and boat ass = A ρ w so ω = (g / ) ½ ighter boats bob ore quicl than heav ones (if the sae sie) Net ( Eaple of phase = A cos(ωt + φ) l You have identical vertical springs with identical asses. Both are undergoing siple haronic otion with frequenc f = 1/π (/) ½ l he 1 st ass alwas oves up when the nd ass is oves down. Vertical displaceent π π 1 st ass / tie =ωt nd ass F B g What is the phase difference between the two asses? A: B: π/ C: π D: 3π/ E: π Phsics 1: ecture 9, Pg 5 Phsics 1: ecture 9, Pg 6 Page 1
2 Phsics 1 ecture 9 he shaer cart l You stand inside a sall cart attached to a heav-dut spring, the spring is copressed and released, and ou shae bac and forth, attepting to aintain our balance. Note that there is also a sandbag in the cart with ou. l At the instant ou pass through the equilibriu position of the spring, ou drop the sandbag out of the cart onto the ground. l What effect does jettisoning the sandbag at the equilibriu position have on the aplitude of our oscillation? A. It increases the aplitude. B. It decreases the aplitude. C. It has no effect on the aplitude. Hint: At equilibriu, both the cart and the bag are oving at he shaer cart l Instead of dropping the sandbag as ou pass through equilibriu, ou decide to drop the sandbag when the cart is at its aiu distance fro equilibriu. l What effect does jettisoning the sandbag at the cart s aiu distance fro equilibriu have on the aplitude of our oscillation? A. It increases the aplitude. B. It decreases the aplitude. C. It has no effect on the aplitude. Hint: At aiu displaceent there is no inetic energ. their aiu speed. Phsics 1: ecture 9, Pg 7 Phsics 1: ecture 9, Pg 8 he shaer cart l What effect does jettisoning the sandbag at the cart s aiu displaceent fro equilibriu have on the aiu speed of the cart? A. It increases the aiu speed. B. It decreases the aiu speed. C. It has no effect on the aiu speed. Hint: At aiu displaceent there is no inetic energ. Phsics 1: ecture 9, Pg 9 he Pendulu (using torque) l A pendulu is ade b suspending a ass at the end of a string of length. Find the frequenc of oscillation for sall displaceents. sin Σ τ = Iα = -g sin() Σ τ α -g (d / ) = -g copare to a = - d / = (-g/) with (t)= cos( ωt + φ ) and ω =(g/) ½ g Phsics 1: ecture 9, Pg 1 he Pendulu l A pendulu is ade b suspending a ass at the end of a string of length. Find the frequenc of oscillation for sall displaceents. he Siple Pendulu l A pendulu is ade b suspending a ass at the end of a string of length. Find the frequenc of oscillation for sall displaceents. If sall then sin() tan. = sin. =. 5 tan.9 = sin.9 =.9 1 tan.17 = sin.17 = tan.6 =.7 sin.6 =.6 Σ F = a = g cos() = a c = v / Σ F = a = -g sin() where = tan If sall then and sin() d/ = d/ a = d / = d / so a = -g = d / d / - g = g Phsics 1: ecture 9, Pg 11 and = cos(ωt + φ) or = sin(ωt + φ) with ω = (g/) ½ g Phsics 1: ecture 9, Pg 1 Page
3 Phsics 1 ecture 9 What about Vertical Springs? l For a vertical spring, if is easured fro the equilibriu position U = 1 l ecall: force of the spring is the negative derivative of this function: du F = = d l his will be just lie the horiontal case: d - = a = Which has solution (t) = A cos( ωt + φ) where ω = Phsics 1: ecture 9, Pg 13 j = F= - Eercise Siple Haronic Motion l A ass oscillates up & down on a spring. It s position as a function of tie is shown below. At which of the points shown does the ass have positive velocit and negative acceleration? eeber: velocit is slope and acceleration is the curvature (a) (t) (b) (c) t Phsics 1: ecture 9, Pg 14 Eaple l A ass = g on a spring oscillates with aplitude A = 1 c. At t = its speed is at a aiu, and is v=+ /s v What is the angular frequenc of oscillation ω? v What is the spring constant? General relationships E = K + U = constant, ω = (/) ½ So at aiu speed U= and ½ v = E = ½ A thus = v /A = () /(.1) = 8 N/, ω = rad/sec Phsics 1: ecture 9, Pg 15 Eaple Initial Conditions l A ass hanging fro a vertical spring is lifted a distance d above equilibriu and released at t =. Which of the following describe its velocit and acceleration as a function of tie (upwards is positive direction): (A) v(t) = - v a sin( ωt ) a(t) = -a a cos( ωt ) (B) v(t) = v a sin( ωt ) a(t) = a a cos( ωt ) t = (C) v(t) = v a cos( ωt ) a(t) = -a a cos(ωt ) (both v a and a a are positive nubers) d Phsics 1: ecture 9, Pg 16 Eercise Initial Conditions l A ass hanging fro a vertical spring is lifted a distance d above equilibriu and released at t =. Which of the following describe its velocit and acceleration as a function of tie (upwards is positive direction): (A) v(t) = - v a sin( ωt ) a(t) = -a a cos( ωt ) Eercise Siple Haronic Motion l You are sitting on a swing. A friend gives ou a sall push and ou start swinging bac & forth with period 1. l Suppose ou were standing on the swing rather than sitting. When given a sall push ou start swinging bac & forth with period. (B) v(t) = v a sin( ωt ) a(t) = a a cos( ωt ) t = (C) v(t) = v a cos( ωt ) a(t) = -a a cos(ωt ) (both v a and a a are positive nubers) d Which of the following is true recalling that ω = (g/) ½ (A) 1 = (B) 1 > (C) 1 < Phsics 1: ecture 9, Pg 17 Phsics 1: ecture 9, Pg 18 Page 3
4 Phsics 1 ecture 9 A od Pendulu l A pendulu is ade b suspending a thin rod of length and ass M at one end. Find the frequenc of oscillation for sall displaceents. Σ τ = I α = - r F = (/) g sin() I rod at end = /3 - /3 α / g -1/3 d / = ½ g CM ω = 3 g g General Phsical Pendulu l Suppose we have soe arbitraril shaped solid of ass M hung on a fied ais, that we now where the CM is located and what the oent of inertia I about the ais is. l he torque about the rotation () ais for sall is (sin ) d τ = Mg = I -Mg sin -Mg d = ω where ω = Mg I = cos(ωt + φ) τ α -ais CM Mg Phsics 1: ecture 9, Pg 19 Phsics 1: ecture 9, Pg orsion Pendulu l Consider an object suspended b a wire attached at its CM. he wire defines the rotation ais, and the oent of inertia I about this ais is nown. l he wire acts lie a rotational spring. v When the object is rotated, the wire is twisted. his produces a torque that opposes the rotation. v orque is proportional to the angular displaceent: τ = - κ where κ is the torsion constant v ω = (κ/i) ½ τ I wire Eercise Period l All of the following torsional pendulu bobs have the sae ass and radius with ω = (κ/i) ½ l Which pendulu rotates the slowest (i.e. has the longest period) if the wires are identical? (A) (B) (C) (D) Phsics 1: ecture 9, Pg 1 Phsics 1: ecture 9, Pg What about Friction? A velocit dependent drag force (A odel) d d b = d b d + + = We can guess at a new solution. ( t) = A ep( bt ) cos( ω t + φ ) and now ω Note / What about Friction? A daped eponential ( t) = A ep( b t) cos ( ω t + φ ) if A ωo > b / -. With, ω = b = ω o b ωt Phsics 1: ecture 9, Pg 3 Phsics 1: ecture 9, Pg 4 Page 4
5 Phsics 1 ecture 9 Variations in the daping Daped Siple Haronic Motion ω = ω o ( b / ) Sall daping tie constant (/b) ow friction coefficient, b << l A downward shift in the angular frequenc l here are three atheaticall distinct regies ωo > b / ωo = b / ωo < b / Moderate daping tie constant (/b) Moderate friction coefficient (b < ) Phsics 1: ecture 9, Pg 5 underdaped criticall daped overdaped Phsics 1: ecture 9, Pg 6 Eercise l Daped oscillations: A can of coe is attached to a spring and is displaced b hand ( =.5 g & = 5. N/) he coe can is released, and it starts oscillating with an aplitude of A =.3. How daped is the sste? A. Underdaped (ultiple oscillations with an eponential deca in aplitude) B. Criticall daped (siple decaing otion with at ost one overshoot of the sste's resting position) C. Overdaped (siple eponentiall decaing otion, without an oscillations) Phsics 1: ecture 9, Pg 7 Driven SHM with esistance l Appl a sinusoidal force, F cos (ωt), and now consider what A and b do, d b d F + + = cos ωt Not Zero!!! F / A = bω b/ sall ( ω ω ) + ( ) stead state aplitude b/ iddling b large ω ω ω Phsics 1: ecture 9, Pg 8 For hursda l eview for final! Phsics 1: ecture 9, Pg 9 Page 5
Physics 207 Lecture 18. Physics 207, Lecture 18, Nov. 3 Goals: Chapter 14
Physics 07, Lecture 18, Nov. 3 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand
More informationPHYS 1443 Section 003 Lecture #22
PHYS 443 Section 003 Lecture # Monda, Nov. 4, 003. Siple Bloc-Spring Sste. Energ of the Siple Haronic Oscillator 3. Pendulu Siple Pendulu Phsical Pendulu orsion Pendulu 4. Siple Haronic Motion and Unifor
More informationUnit 14 Harmonic Motion. Your Comments
Today s Concepts: Periodic Motion Siple - Mass on spring Daped Forced Resonance Siple - Pendulu Unit 1, Slide 1 Your Coents Please go through the three equations for siple haronic otion and phase angle
More informationSimple Harmonic Motion
Siple Haronic Motion Physics Enhanceent Prograe for Gifted Students The Hong Kong Acadey for Gifted Education and Departent of Physics, HKBU Departent of Physics Siple haronic otion In echanical physics,
More informationLecture #8-3 Oscillations, Simple Harmonic Motion
Lecture #8-3 Oscillations Siple Haronic Motion So far we have considered two basic types of otion: translation and rotation. But these are not the only two types of otion we can observe in every day life.
More informationPY241 Solutions Set 9 (Dated: November 7, 2002)
PY241 Solutions Set 9 (Dated: Noveber 7, 2002) 9-9 At what displaceent of an object undergoing siple haronic otion is the agnitude greatest for the... (a) velocity? The velocity is greatest at x = 0, the
More informationCHECKLIST. r r. Newton s Second Law. natural frequency ω o (rad.s -1 ) (Eq ) a03/p1/waves/waves doc 9:19 AM 29/03/05 1
PHYS12 Physics 1 FUNDAMENTALS Module 3 OSCILLATIONS & WAVES Text Physics by Hecht Chapter 1 OSCILLATIONS Sections: 1.5 1.6 Exaples: 1.6 1.7 1.8 1.9 CHECKLIST Haronic otion, periodic otion, siple haronic
More informationPeriodic Motion is everywhere
Lecture 19 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand and use energy conservation
More informationSimple Harmonic Motion
Reading: Chapter 15 Siple Haronic Motion Siple Haronic Motion Frequency f Period T T 1. f Siple haronic otion x ( t) x cos( t ). Aplitude x Phase Angular frequency Since the otion returns to its initial
More informationOscillations: Review (Chapter 12)
Oscillations: Review (Chapter 1) Oscillations: otions that are periodic in tie (i.e. repetitive) o Swinging object (pendulu) o Vibrating object (spring, guitar string, etc.) o Part of ediu (i.e. string,
More informationQ5 We know that a mass at the end of a spring when displaced will perform simple m harmonic oscillations with a period given by T = 2!
Chapter 4.1 Q1 n oscillation is any otion in which the displaceent of a particle fro a fixed point keeps changing direction and there is a periodicity in the otion i.e. the otion repeats in soe way. In
More information= T. Oscillations and Waves. Example of an Oscillating System IB 12 IB 12
Oscillation: the vibration of an object Oscillations and Waves Eaple of an Oscillating Syste A ass oscillates on a horizontal spring without friction as shown below. At each position, analyze its displaceent,
More informationMore Oscillations! (Today: Harmonic Oscillators)
More Oscillations! (oday: Haronic Oscillators) Movie assignent reinder! Final due HURSDAY April 20 Subit through ecapus Different rubric; reeber to chec it even if you got 00% on your draft: http://sarahspolaor.faculty.wvu.edu/hoe/physics-0
More information5/09/06 PHYSICS 213 Exam #1 NAME FEYNMAN Please write down your name also on the back side of the last page
5/09/06 PHYSICS 13 Exa #1 NAME FEYNMAN Please write down your nae also on the back side of the last page 1 he figure shows a horizontal planks of length =50 c, and ass M= 1 Kg, pivoted at one end. he planks
More informationm A 1 m mgd k m v ( C) AP Physics Multiple Choice Practice Oscillations
P Physics Multiple Choice Practice Oscillations. ass, attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is.
More informationT m. Fapplied. Thur Oct 29. ω = 2πf f = (ω/2π) T = 1/f. k m. ω =
Thur Oct 9 Assignent 10 Mass-Spring Kineatics (x, v, a, t) Dynaics (F,, a) Tie dependence Energy Pendulu Daping and Resonances x Acos( ωt) = v = Aω sin( ωt) a = Aω cos( ωt) ω = spring k f spring = 1 k
More informationwhich proves the motion is simple harmonic. Now A = a 2 + b 2 = =
Worked out Exaples. The potential energy function for the force between two atos in a diatoic olecules can be expressed as follows: a U(x) = b x / x6 where a and b are positive constants and x is the distance
More informationPHY 140Y FOUNDATIONS OF PHYSICS Tutorial Questions #9 Solutions November 12/13
PHY 4Y FOUNDAIONS OF PHYSICS - utorial Questions #9 Solutions Noveber /3 Conservation of Ener and Sprins. One end of a assless sprin is placed on a flat surface, with the other end pointin upward, as shown
More informationPhysics 2107 Oscillations using Springs Experiment 2
PY07 Oscillations using Springs Experient Physics 07 Oscillations using Springs Experient Prelab Read the following bacground/setup and ensure you are failiar with the concepts and theory required for
More informationPhysics 41 HW Set 1 Chapter 15 Serway 7 th Edition
Physics HW Set Chapter 5 Serway 7 th Edition Conceptual Questions:, 3, 5,, 6, 9 Q53 You can take φ = π, or equally well, φ = π At t= 0, the particle is at its turning point on the negative side of equilibriu,
More informationPage 1. Physics 131: Lecture 22. Today s Agenda. SHM and Circles. Position
Physics 3: ecture Today s genda Siple haronic otion Deinition Period and requency Position, velocity, and acceleration Period o a ass on a spring Vertical spring Energy and siple haronic otion Energy o
More informationA body of unknown mass is attached to an ideal spring with force constant 123 N/m. It is found to vibrate with a frequency of
Chapter 14 [ Edit ] Overview Suary View Diagnostics View Print View with Answers Chapter 14 Due: 11:59p on Sunday, Noveber 27, 2016 To understand how points are awarded, read the Grading Policy for this
More informationWileyPLUS Assignment 3. Next Week
WileyPLUS Assignent 3 Chapters 6 & 7 Due Wednesday, Noveber 11 at 11 p Next Wee No labs of tutorials Reebrance Day holiday on Wednesday (no classes) 24 Displaceent, x Mass on a spring ωt = 2π x = A cos
More informationStudent Book pages
Chapter 7 Review Student Boo pages 390 39 Knowledge. Oscillatory otion is otion that repeats itself at regular intervals. For exaple, a ass oscillating on a spring and a pendulu swinging bac and forth..
More informationCHAPTER 15: Vibratory Motion
CHAPTER 15: Vibratory Motion courtesy of Richard White courtesy of Richard White 2.) 1.) Two glaring observations can be ade fro the graphic on the previous slide: 1.) The PROJECTION of a point on a circle
More informationSIMPLE HARMONIC MOTION: NEWTON S LAW
SIMPLE HARMONIC MOTION: NEWTON S LAW siple not siple PRIOR READING: Main 1.1, 2.1 Taylor 5.1, 5.2 http://www.yoops.org/twocw/it/nr/rdonlyres/physics/8-012fall-2005/7cce46ac-405d-4652-a724-64f831e70388/0/chp_physi_pndul.jpg
More informationPH 221-1D Spring Oscillations. Lectures Chapter 15 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition)
PH 1-1D Spring 013 Oscillations Lectures 35-37 Chapter 15 (Halliday/Resnick/Walker, Fundaentals of Physics 9 th edition) 1 Chapter 15 Oscillations In this chapter we will cover the following topics: Displaceent,
More informationPhysics 207: Lecture 26. Announcements. Make-up labs are this week Final hwk assigned this week, final quiz next week.
Torque due to gravit Rotation Recap Phsics 07: ecture 6 Announceents Make-up labs are this week Final hwk assigned this week, final quiz net week Toda s Agenda Statics Car on a Hill Static Equilibriu Equations
More information27 Oscillations: Introduction, Mass on a Spring
Chapter 7 Oscillations: Introduction, Mass on a Spring 7 Oscillations: Introduction, Mass on a Spring If a siple haronic oscillation proble does not involve the tie, you should probably be using conservation
More informationOSCILLATIONS AND WAVES
OSCILLATIONS AND WAVES OSCILLATION IS AN EXAMPLE OF PERIODIC MOTION No stories this tie, we are going to get straight to the topic. We say that an event is Periodic in nature when it repeats itself in
More informationSimple and Compound Harmonic Motion
Siple Copound Haronic Motion Prelab: visit this site: http://en.wiipedia.org/wii/noral_odes Purpose To deterine the noral ode frequencies of two systes:. a single ass - two springs syste (Figure );. two
More informationTOPIC E: OSCILLATIONS SPRING 2018
TOPIC E: OSCILLATIONS SPRING 018 1. Introduction 1.1 Overview 1. Degrees of freedo 1.3 Siple haronic otion. Undaped free oscillation.1 Generalised ass-spring syste: siple haronic otion. Natural frequency
More informationProblem Set 14: Oscillations AP Physics C Supplementary Problems
Proble Set 14: Oscillations AP Physics C Suppleentary Probles 1 An oscillator consists of a bloc of ass 050 g connected to a spring When set into oscillation with aplitude 35 c, it is observed to repeat
More informationUSEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS. By: Ian Blokland, Augustana Campus, University of Alberta
1 USEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS By: Ian Bloland, Augustana Capus, University of Alberta For: Physics Olypiad Weeend, April 6, 008, UofA Introduction: Physicists often attept to solve
More informationExperiment 2: Hooke s Law
COMSATS Institute of Inforation Technology, Islaabad Capus PHYS-108 Experient 2: Hooke s Law Hooke s Law is a physical principle that states that a spring stretched (extended) or copressed by soe distance
More informationSHM stuff the story continues
SHM stuff the story continues Siple haronic Motion && + ω solution A cos t ( ω + α ) Siple haronic Motion + viscous daping b & + ω & + Viscous daping force A e b t Viscous daped aplitude Viscous daped
More information1B If the stick is pivoted about point P a distance h = 10 cm from the center of mass, the period of oscillation is equal to (in seconds)
05/07/03 HYSICS 3 Exa #1 Use g 10 /s in your calculations. NAME Feynan lease write your nae also on the back side of this exa 1. 1A A unifor thin stick of ass M 0. Kg and length 60 c is pivoted at one
More informationPHYS 102 Previous Exam Problems
PHYS 102 Previous Exa Probles CHAPTER 16 Waves Transverse waves on a string Power Interference of waves Standing waves Resonance on a string 1. The displaceent of a string carrying a traveling sinusoidal
More informationChapter 14: Periodic motion
Chapter 14: Periodic motion Describing oscillations Simple harmonic motion Energy of simple harmonic motion Applications of simple harmonic motion Simple pendulum & physical pendulum Damped oscillations
More informationPhysics 2210 Fall smartphysics 20 Conservation of Angular Momentum 21 Simple Harmonic Motion 11/23/2015
Physics 2210 Fall 2015 sartphysics 20 Conservation of Angular Moentu 21 Siple Haronic Motion 11/23/2015 Exa 4: sartphysics units 14-20 Midter Exa 2: Day: Fri Dec. 04, 2015 Tie: regular class tie Section
More information9 HOOKE S LAW AND SIMPLE HARMONIC MOTION
Experient 9 HOOKE S LAW AND SIMPLE HARMONIC MOTION Objectives 1. Verify Hoo s law,. Measure the force constant of a spring, and 3. Measure the period of oscillation of a spring-ass syste and copare it
More informationTUTORIAL 1 SIMPLE HARMONIC MOTION. Instructor: Kazumi Tolich
TUTORIAL 1 SIMPLE HARMONIC MOTION Instructor: Kazui Tolich About tutorials 2 Tutorials are conceptual exercises that should be worked on in groups. Each slide will consist of a series of questions that
More informationLecture XXVI. Morris Swartz Dept. of Physics and Astronomy Johns Hopkins University November 5, 2003
Lecture XXVI Morris Swartz Dept. of Physics and Astronomy Johns Hopins University morris@jhu.edu November 5, 2003 Lecture XXVI: Oscillations Oscillations are periodic motions. There are many examples of
More information. The maximum speed m can be doubled by doubling the amplitude, A. 5. The maximum speed of a simple harmonic oscillator is given by v = A
CHAPTER 4: Oscillations Responses to Questions. Exaples are: a child s swing (SHM, for sall oscillations), stereo speaers (coplicated otion, the addition of any SHMs), the blade on a jigsaw (approxiately
More informationSimple Harmonic Motion of Spring
Nae P Physics Date iple Haronic Motion and prings Hooean pring W x U ( x iple Haronic Motion of pring. What are the two criteria for siple haronic otion? - Only restoring forces cause siple haronic otion.
More informationChapter 15 Periodic Motion
Chapter 15 Periodic Motion Slide 1-1 Chapter 15 Periodic Motion Concepts Slide 1-2 Section 15.1: Periodic motion and energy Section Goals You will learn to Define the concepts of periodic motion, vibration,
More informationPHYS 1443 Section 003 Lecture #21 Wednesday, Nov. 19, 2003 Dr. Mystery Lecturer
PHYS 443 Section 003 Lecture # Wednesday, Nov. 9, 003 Dr. Mystery Lecturer. Fluid Dyanics : Flow rate and Continuity Equation. Bernoulli s Equation 3. Siple Haronic Motion 4. Siple Bloc-Spring Syste 5.
More informationIn the session you will be divided into groups and perform four separate experiments:
Mechanics Lab (Civil Engineers) Nae (please print): Tutor (please print): Lab group: Date of lab: Experients In the session you will be divided into groups and perfor four separate experients: (1) air-track
More informationL 2. AP Physics Free Response Practice Oscillations ANSWERS 1975B7. (a) F T2. (b) F NET(Y) = 0
AP Physics Free Response Practice Oscillations ANSWERS 1975B7. (a) 60 F 1 F g (b) F NE(Y) = 0 F1 F1 = g / cos(60) = g (c) When the string is cut it swings fro top to botto, siilar to the diagra for 1974B1
More information5.2. Example: Landau levels and quantum Hall effect
68 Phs460.nb i ħ (-i ħ -q A') -q φ' ψ' = + V(r) ψ' (5.49) t i.e., using the new gauge, the Schrodinger equation takes eactl the sae for (i.e. the phsics law reains the sae). 5.. Eaple: Lau levels quantu
More informationPearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world
Pearson Education Liited Edinburgh Gate Harlow Esse CM0 JE England and Associated Copanies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk Pearson Education Liited 04 All rights
More informationPhysics 4A Solutions to Chapter 15 Homework
Physics 4A Solutions to Chapter 15 Hoework Chapter 15 Questions:, 8, 1 Exercises & Probles 6, 5, 31, 41, 59, 7, 73, 88, 90 Answers to Questions: Q 15- (a) toward -x (b) toward +x (c) between -x and 0 (d)
More informationVIBRATING SYSTEMS. example. Springs obey Hooke s Law. Terminology. L 21 Vibration and Waves [ 2 ]
L 1 Vibration and Waves [ ] Vibrations (oscillations) resonance pendulu springs haronic otion Waves echanical waves sound waves usical instruents VIBRATING SYSTEMS Mass and spring on air trac Mass hanging
More informationClassical Mechanics Small Oscillations
Classical Mechanics Sall Oscillations Dipan Kuar Ghosh UM-DAE Centre for Excellence in Basic Sciences, Kalina Mubai 400098 Septeber 4, 06 Introduction When a conservative syste is displaced slightly fro
More informationQuestion number 1 to 8 carries 2 marks each, 9 to 16 carries 4 marks each and 17 to 18 carries 6 marks each.
IIT-JEE5-PH-1 FIITJEE Solutions to IITJEE 5 Mains Paper Tie: hours Physics Note: Question nuber 1 to 8 carries arks each, 9 to 16 carries 4 arks each and 17 to 18 carries 6 arks each. Q1. whistling train
More informationOscillations Equations 0. Out of the followin functions representin otion of a particle which represents SHM I) y = sinωt cosωt 3 II) y = sin ωt III) IV) 3 y = 5cos 3ωt 4 y = + ωt+ ω t a) Only IV does
More information(b) Frequency is simply the reciprocal of the period: f = 1/T = 2.0 Hz.
Chapter 5. (a) During siple haronic otion, the speed is (oentarily) zero when the object is at a turning point (that is, when x = +x or x = x ). Consider that it starts at x = +x and we are told that t
More informationOscillations. Oscillations and Simple Harmonic Motion
Oscillations AP Physics C Oscillations and Simple Harmonic Motion 1 Equilibrium and Oscillations A marble that is free to roll inside a spherical bowl has an equilibrium position at the bottom of the bowl
More informationChapter 14 Periodic Motion
Chapter 14 Periodic Motion 1 Describing Oscillation First, we want to describe the kinematical and dynamical quantities associated with Simple Harmonic Motion (SHM), for example, x, v x, a x, and F x.
More informationChapter 15 - Oscillations
The pendulum of the mind oscillates between sense and nonsense, not between right and wrong. -Carl Gustav Jung David J. Starling Penn State Hazleton PHYS 211 Oscillatory motion is motion that is periodic
More informationOscillatory Motion SHM
Chapter 15 Oscillatory Motion SHM Dr. Armen Kocharian Periodic Motion Periodic motion is motion of an object that regularly repeats The object returns to a given position after a fixed time interval A
More information1 k. 1 m. m A. AP Physics Multiple Choice Practice Work-Energy
AP Physics Multiple Choice Practice Wor-Energy 1. A ass attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is
More informationChapter 11 Simple Harmonic Motion
Chapter 11 Siple Haronic Motion "We are to adit no ore causes of natural things than such as are both true and sufficient to explain their appearances." Isaac Newton 11.1 Introduction to Periodic Motion
More informationP235 Midterm Examination Prof. Cline
P235 Mier Exaination Prof. Cline THIS IS A CLOSED BOOK EXAMINATION. Do all parts of all four questions. Show all steps to get full credit. 7:00-10.00p, 30 October 2009 1:(20pts) Consider a rocket fired
More information4.7. Springs and Conservation of Energy. Conservation of Mechanical Energy
Springs and Conservation of Energy Most drivers try to avoid collisions, but not at a deolition derby like the one shown in Figure 1. The point of a deolition derby is to crash your car into as any other
More informationClassical Mechanics Lecture 22
Classical Mechanics Lecture 22 Today s Concept: Siple Haronic Mo7on: Mo#on of a Pendulu Mechanics Lecture 8, Slide 1 Grading Unit 14 and 15 Ac7vity Guides will not be graded Please turn in:! Unit 14 WriIen
More informationPage 1. Physics 131: Lecture 22. SHM and Circles. Today s Agenda. Position. Velocity. Position and Velocity. Acceleration. v Asin.
Physics 3: ecture Today s enda Siple haronic otion Deinition Period and requency Position, velocity, and acceleration Period o a ass on a sprin Vertical sprin Enery and siple haronic otion Enery o a sprin
More informationPhysics 18 Spring 2011 Homework 3 - Solutions Wednesday February 2, 2011
Phsics 18 Spring 2011 Hoework 3 - s Wednesda Februar 2, 2011 Make sure our nae is on our hoework, and please bo our final answer. Because we will be giving partial credit, be sure to attept all the probles,
More informationSimple Harmonic Motion
Simple Harmonic Motion (FIZ 101E - Summer 2018) July 29, 2018 Contents 1 Introduction 2 2 The Spring-Mass System 2 3 The Energy in SHM 5 4 The Simple Pendulum 6 5 The Physical Pendulum 8 6 The Damped Oscillations
More informationTutorial Exercises: Incorporating constraints
Tutorial Exercises: Incorporating constraints 1. A siple pendulu of length l ass is suspended fro a pivot of ass M that is free to slide on a frictionless wire frae in the shape of a parabola y = ax. The
More informationPhysics 207 Lecture 24
Physics 7 Lecture 4 Physics 7, Lecture 4, Nov. 7 gena: Mi-Ter 3 Review Elastic Properties of Matter, Mouli Pressure, Wor, rchiees Principle, Flui flow, Bernoulli Oscillatory otion, Linear oscillator, Penulus
More information3. Period Law: Simplified proof for circular orbits Equate gravitational and centripetal forces
Physics 106 Lecture 10 Kepler s Laws and Planetary Motion-continued SJ 7 th ed.: Chap 1., 1.6 Kepler s laws of planetary otion Orbit Law Area Law Period Law Satellite and planetary orbits Orbits, potential,
More informationChapter 1: Basics of Vibrations for Simple Mechanical Systems
Chapter 1: Basics of Vibrations for Siple Mechanical Systes Introduction: The fundaentals of Sound and Vibrations are part of the broader field of echanics, with strong connections to classical echanics,
More information2009 Academic Challenge
009 Acadeic Challenge PHYSICS TEST - REGIONAL This Test Consists of 5 Questions Physics Test Production Tea Len Stor, Eastern Illinois University Author/Tea Leader Doug Brandt, Eastern Illinois University
More informationLecture 4 Normal Modes
Lecture 4 Noral Modes Coupled driven oscillators Double pendulu The daped driven pendulu = g/l +k y+fcost y = y gy/l k y d dt + d dt + g + k l k k d dt + d dt + g + k l y = F 0 Re eit y =Re X Y eit CF
More informationOscillations. PHYS 101 Previous Exam Problems CHAPTER. Simple harmonic motion Mass-spring system Energy in SHM Pendulums
PHYS 101 Previous Exam Problems CHAPTER 15 Oscillations Simple harmonic motion Mass-spring system Energy in SHM Pendulums 1. The displacement of a particle oscillating along the x axis is given as a function
More informationPhysics 120 Final Examination
Physics 120 Final Exaination 12 August, 1998 Nae Tie: 3 hours Signature Calculator and one forula sheet allowed Student nuber Show coplete solutions to questions 3 to 8. This exaination has 8 questions.
More informationOSCILLATIONS CHAPTER FOURTEEN 14.1 INTRODUCTION
CHAPTER FOURTEEN OSCILLATIONS 14.1 INTRODUCTION 14.1 Introduction 14. Periodic and oscilatory otions 14.3 Siple haronic otion 14.4 Siple haronic otion and unifor circular otion 14.5 Velocity and acceleration
More informationClassical Mechanics Lecture 22
Classical Mechanics Lecture 22 Today s Concept: Siple Haronic Mo7on: Mo#on of a Pendulu Mechanics Lecture 8, Slide 1 Your Coents so the oega can stand for both the oscilla7on frequency or angular velocity
More information( ) ( ) 1. (a) The amplitude is half the range of the displacement, or x m = 1.0 mm.
1. (a) The aplitude is half the range of the displaceent, or x = 1.0. (b) The axiu speed v is related to the aplitude x by v = ωx, where ω is the angular frequency. Since ω = πf, where f is the frequency,
More informationQuestion 1. [14 Marks]
6 Question 1. [14 Marks] R r T! A string is attached to the dru (radius r) of a spool (radius R) as shown in side and end views here. (A spool is device for storing string, thread etc.) A tension T is
More informationPHYSICS ADVANCED LABORATORY I UNIVERSAL GRAVITATIONAL CONSTANT Spring 2001
PHYSICS 334 - ADVANCED LABOATOY I UNIVESAL GAVITATIONAL CONSTANT Spring 001 Purposes: Deterine the value of the universal gravitation constant G. Backgroun: Classical echanics topics-oents of inertia,
More informationChapter 13: Oscillatory Motions
Chapter 13: Oscillatory Motions Simple harmonic motion Spring and Hooe s law When a mass hanging from a spring and in equilibrium, the Newton s nd law says: Fy ma Fs Fg 0 Fs Fg This means the force due
More informationEnergy and Momentum: The Ballistic Pendulum
Physics Departent Handout -10 Energy and Moentu: The Ballistic Pendulu The ballistic pendulu, first described in the id-eighteenth century, applies principles of echanics to the proble of easuring the
More informationSRI LANKAN PHYSICS OLYMPIAD MULTIPLE CHOICE TEST 30 QUESTIONS ONE HOUR AND 15 MINUTES
SRI LANKAN PHYSICS OLYMPIAD - 5 MULTIPLE CHOICE TEST QUESTIONS ONE HOUR AND 5 MINUTES INSTRUCTIONS This test contains ultiple choice questions. Your answer to each question ust be arked on the answer sheet
More informationDepartment of Physics Preliminary Exam January 3 6, 2006
Departent of Physics Preliinary Exa January 3 6, 2006 Day 1: Classical Mechanics Tuesday, January 3, 2006 9:00 a.. 12:00 p.. Instructions: 1. Write the answer to each question on a separate sheet of paper.
More informationm A 9. The length of a simple pendulum with a period on Earth of one second is most nearly (A) 0.12 m (B) 0.25 m (C) 0.50 m (D) 1.0 m (E) 10.
P Physics Multiple Choice Practice Oscillations. ass, attache to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu isplaceent fro its equilibriu position is. What
More informationChapter 14 Oscillations. Copyright 2009 Pearson Education, Inc.
Chapter 14 Oscillations Oscillations of a Spring Simple Harmonic Motion Energy in the Simple Harmonic Oscillator Simple Harmonic Motion Related to Uniform Circular Motion The Simple Pendulum The Physical
More information8.1 Force Laws Hooke s Law
8.1 Force Laws There are forces that don't change appreciably fro one instant to another, which we refer to as constant in tie, and forces that don't change appreciably fro one point to another, which
More informationClassical Mechanics Lecture 22
Classical Mechanics Lecture 22 Today s Concept: Siple Haronic Mo7on: Mo#on of a Pendulu Mechanics Lecture 8, Slide 1 Grading Unit 14 and 15 Ac7vity Guides will not be graded Please turn in:! Unit 14 WriEen
More informationAnnouncements. Last year s final exam has been posted. Final exam is worth 200 points and is 2 hours: Quiz #9 this Wednesday:
Announceents sartphysics hoework deadlines have been reset to :0 PM on eceber 15 (beinnin of final exa). You can et 100% credit if you o back and correct ANY proble on the HW fro the beinnin of the seester!
More informationMass on a Horizontal Spring
Course- B.Sc. Applied Physical Science (Computer Science) Year- IInd, Sem- IVth Subject Physics Paper- XIVth, Electromagnetic Theory Lecture No. 22, Simple Harmonic Motion Introduction Hello friends in
More informationJOURNAL OF PHYSICAL AND CHEMICAL SCIENCES
JOURNAL OF PHYSIAL AND HEMIAL SIENES Journal hoepage: http://scienceq.org/journals/jps.php Review Open Access A Review of Siple Haronic Motion for Mass Spring Syste and Its Analogy to the Oscillations
More informationDamped Harmonic Motion
Daped Haronic Motion PY154 Special Topics in Physics PY154 1 Driven Daped Haronic Motion What if we apply a haronic force?: F h Be it The total force is then: dx F Fh kx b dt d x dt Assue a solution of
More informationPeriodic Motion. Periodic motion is motion of an object that. regularly repeats
Periodic Motion Periodic motion is motion of an object that regularly repeats The object returns to a given position after a fixed time interval A special kind of periodic motion occurs in mechanical systems
More informationChapter 15. Oscillations
Chapter 15 Oscillations 15.1 Simple Harmonic Motion Oscillatory Motion: Motion which is periodic in time; motion that repeats itself in time. Examples: SHM: Power line oscillates when the wind blows past.
More informationCE573 Structural Dynamics [Fall 2008]
CE573 Structural Dynaics [Fall 2008] 1) A rigid vehicle weighing 2000 lb, oving horizontally at a velocity of 12 ft/sec, is stopped by a barrier consisting of wire ropes stretched between two rigid anchors
More informationChapter 5, Conceptual Questions
Chapter 5, Conceptual Questions 5.1. Two forces are present, tension T in the cable and gravitational force 5.. F G as seen in the figure. Four forces act on the block: the push of the spring F, sp gravitational
More informationFor a situation involving gravity near earth s surface, a = g = jg. Show. that for that case v 2 = v 0 2 g(y y 0 ).
Reading: Energy 1, 2. Key concepts: Scalar products, work, kinetic energy, work-energy theore; potential energy, total energy, conservation of echanical energy, equilibriu and turning points. 1.! In 1-D
More informationBALLISTIC PENDULUM. EXPERIMENT: Measuring the Projectile Speed Consider a steel ball of mass
BALLISTIC PENDULUM INTRODUCTION: In this experient you will use the principles of conservation of oentu and energy to deterine the speed of a horizontally projected ball and use this speed to predict the
More information