Waves and Fields (PHYS 195): Week 4 Spring 2019 v1.0
|
|
- Corey Mosley
- 5 years ago
- Views:
Transcription
1 Waves and Fields (PHYS 195): Week 4 Spring 2019 v1.0 Intro: This week we finish our study of damped driven oscillators and resonance in these systems and start on our study of waves, beginning with transverse waves on a string. The first mid-term is this coming week during lab sections (Feb 21-22). Choose a lab section (Thursday or Friday) to take the midterm. Obviously, there will be not lab this week. Problem sets will not be due this week. Instead the problems on this guide are example mid-term questions. Reading: Friday: HRW Monday: HRW 16.4 Wednesday: HRW Physics Topics: Resonance The dependence of amplitude and phase of driving angular frequency ω Waves - equation of motion Transverse waves Phasors Math Topics: Partial derivatives Wave equation (in 1 dimension) Problems: Practice problems for the upcoming midterm. Solution hints are at the end of this guide. (1) Equations! (a) Write down the equation of motion for a simple harmonic oscillator (b) Circle the angular frequency in the equation. (c) Write the general solution for SHM (2) Sketch the amplitude as a function of driving frequency, for a damped, driven harmonic oscillator. (3) Please correct the following statement: If you drive a damped harmonic oscillator at a driving frequency other than ω o then at late times it oscillates at ω o but the amplitude of the response depends on how close the driving frequency is to the resonance frequency. (4) Using a simple pendulum you find the local acceleration of gravity. After careful data taking you find that the period is T = ± s and the length of the pendulum is l = ± 0.2 cm. (a) What is your result for g? (b) What is the uncertainty δg? (c) Does it agree with g = ± m/s 2? 1
2 2 Please show all your work. (5) A mass m = 60.0 g hangs from a k = 3.30 N/m spring. (a) What is the angular frequency of oscillation? (b) You observe that the mass looses half its amplitude in 10.5 s. What is the general solution for the position of the mass? (c) When t = 0 the mass is at equilibrium and is moving upward at 1.20 m/s. Find the specific solution that describes the motion. (6) You pilot a spacecraft to a black hole with mass M and enter an orbit. At a radial distance from the planet r, your potential energy is ( U(r) = U o R ) R2 + a2 r r 2 where U o, R, and a are all constants and 0 < r <. Assume the spacecraft has a mass m. (a) Find the equilibrium position of the spacecraft. (b) Find the first three non-vanishing terms of the Taylor series around the stable equilibrium point. (c) Find k eff. (d) What is the angular frequency of small oscillations in the radial position of the spacecraft? This means that the spacecraft orbits the black hole at a radius that undergoes simple harmonic motion. (7) A small cuckoo clock has a pendulum 25 cm long with a mass of 11 g. The clock is powered by a 210 g weight which falls 2 m each day. The amplitude of the swing is 0.20 radians. What is the Q of the clock? (8) Many modern towers contain huge damped oscillator systems designed to oscillate at the same frequency as the buildings themselves. For instance the Taipei 101 tower has a 728 ton pendulum built into the 90-87th floors. You can view a video of the relative motion during an earthquake on this same web page. (a) Why are these damped oscillator systems built? (b) In the video the period of oscillation is about 7.1 s. Assuming a lightly damped simple pendulum, find the natural angular frequency. (c) Suppose that in 10 periods the amplitude of oscillation is reduced from the maximum of 1.4 m to 0.80 m. Find the effective damping coefficient b. (9) View the second video showing masses on springs. The display on the function generator is in Hz. (a) Describe what happens during the video. (b) The mass on the super-bouncy mass-on-a-spring is 10.0 g. What is the spring constant? (10) Describe three ways to find Q. Two ways we used on Guide 3, one way in lab. Lab: Mid-Term I! A look ahead... We move onto harmonics and sound next week. To read ahead see the end of Chapter 16 and the beginning of Chapter 17.
3 3 Problem Hints: (1) Equations! (a) (b) That s ω o. (c) d 2 x dt 2 + ω2 ox = 0. x(t) = x m cos(ω o t + ϕ) (2) See your Lorentzian curve, A 2 (f) vs. f, from lab. (3) The second ω o should be an ω - the driving angular frequency - since the damped, driven system oscillates at the driving frequency. Otherwise the statement is correct. (4) g (a) m/s 2 (b) or so 0.02 or 0.01 depending on method (c) Yes (5) SHM (a) /s (b) y(t) = y m e 0.066t cos(7.42t + ϕ) (c) y(t) = 16.2 e 0.066t sin(7.42t) cm (6) SHM in orbits (a) r o = 2a 2 R (b) Taylor series... (c) (d) k eff = U o 8a 6 R 2 Uo ω = 8ma 6 R 2 (7) The Q of the clock is 71. (8) High DDHM: (a) When the tower sways it drives the damped mass-on-a-spring system. (b) The damping removes energy from the building s oscillation, reducing the amplitude of the swaying motion. This is more comfortable for people in the building and reduces strain on the building structure. Without the damping system one could build a less flexible structure to achieve the same end but this requires lots of costly steel. These systems save money. For instance, the system in the Citicorp building in NYC cost $ 1.5 million and is estimated to have saved $ million in 2,800 tones of structural steel which would have been required to stiffen the structure. ω o = 2π 0.88 s1 T (c) Since A(t) = x m e βt we have Hence, A(t 0 ) = x m e βt0 = 1.4 m A(t T ) = x m e βt0+10t = 0.8 m A(t o + 10T ) A(t o ) = e β10t = (1)
4 4 Hence β = ln(1.4/0.8)/(10t ). Using the relation between β and the damping coefficient b, 2m ln ( ) ln 1.75 b = = kg s 1. 10T You may have used a different definition of ton, which is fine. (9) Video 2 (a) The video shows a speaker driving a flexible bar supporting masses on springs. When the driving force is turned on at 2.60 Hz only one oscillator responds with large amplitude. It is in resonance. (b) Since the super bouncy mass is in resonance, then the driving angular frequency is the resonant angular frequency, or ω o for lightly damped systems, k ω = 2πf = ω o = m. So the spring constant is k = 4π 2 mf 2 = 4π 2 (10g)(2.6 Hz) 2.67 N/m where I assumed 3 sig figs. 2 or 4 are also fine. (10) Curve fit (as we did in lab) with ω o /2β, and with E stored ω o / E/ t.
5 5 Handy Relations General: τ = Iα I = r 2 dm F = du dx F B = ρgv The Taylor series of a function f(x) around x = x o is f(x) = f(x o ) + df dx (x x o ) + 1 d 2 f x=xo 2 dx 2 (x x o ) d 3 f x=xo 3! dx 3 (x x o ) x=xo Oscillations: For spring-like SHM ω o = The energy stored in an oscillator is F = kx k m, a simple pendulum ω o = g l, and a physical pendulum ω o = T = 2π ω o and ω = 2πf. E = 1 2 mω2 ox 2 m. A damped harmonic oscillator has the equation of motion The solution is Q = de dt E 1 ω o d 2 x dx + 2β dt2 dt + ω2 ox = 0. ω o 2β = mω o b and A(t) = x m e βt x(t) = x m e βt cos(ω d t + ϕ) with ω d = ω 2 o β 2 ω o. For a driven system at late times x(t) = A(ω) cos[ωt δ(ω)] with ( ) F o /m 2βω A(ω) = and δ(ω) = arctan [(ωo 2 ω 2 ) 2 + 4β 2 ω 2 ] 1/2 ωo 2 ω 2 where β = b/2m. The resonant angular frequency is ω R = ω 2 o 2β 2. ] k eff = d2 U dx 2 x=x o Uncertainty: Add independent uncertainties in quadrature. For addition and subtraction, add the uncertainties, z = x + y or z = x y then δz = δx 2 + δy 2 For multiplication and division then add the relative uncertainties, (δx z = xy or z = x/y then δz ) 2 z = + x ( ) 2 δy y mgh I.
6 6 For a power, multiply the relative uncertainty by the power, i.e. if z = x n then δz z = nδx x. In general for a calculated quantity q = q(x,..., z) then δq = ( q x δx ) ( ) 2 q x δz
Waves and Fields (PHYS 195): Week 9 Spring 2018 v1.5
Waves and Fields (PHYS 195): Week 9 Spring 2018 v1.5 Intro: This week we finish our discussion of electric potential and electrostatics before moving on to current and a bit of magnetostatics. Reminder:
More informationPreClass Notes: Chapter 13, Sections
PreClass Notes: Chapter 13, Sections 13.3-13.7 From Essential University Physics 3 rd Edition by Richard Wolfson, Middlebury College 2016 by Pearson Education, Inc. Narration and extra little notes by
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 informationOscillations. Simple Harmonic Motion of a Mass on a Spring The equation of motion for a mass m is attached to a spring of constant k is
Dr. Alain Brizard College Physics I (PY 10) Oscillations Textbook Reference: Chapter 14 sections 1-8. Simple Harmonic Motion of a Mass on a Spring The equation of motion for a mass m is attached to a spring
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
Chapter 15 Oscillations Summary Simple harmonic motion Hook s Law Energy F = kx Pendulums: Simple. Physical, Meter stick Simple Picture of an Oscillation x Frictionless surface F = -kx x SHM in vertical
More informationChapter 16: Oscillations
Chapter 16: Oscillations Brent Royuk Phys-111 Concordia University Periodic Motion Periodic Motion is any motion that repeats itself. The Period (T) is the time it takes for one complete cycle of motion.
More informationPHYSICS - CLUTCH CH 15: PERIODIC MOTION (NEW)
!! www.clutchprep.com CONCEPT: Hooke s Law & Springs When you push/pull against a spring (FA), spring pushes back in the direction. (Action-Reaction!) Fs = FA = Ex. 1: You push on a spring with a force
More informationUnit 7: Oscillations
Text: Chapter 15 Unit 7: Oscillations NAME: Problems (p. 405-412) #1: 1, 7, 13, 17, 24, 26, 28, 32, 35 (simple harmonic motion, springs) #2: 45, 46, 49, 51, 75 (pendulums) Vocabulary: simple harmonic motion,
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 informationPhysics 141, Lecture 7. Outline. Course Information. Course information: Homework set # 3 Exam # 1. Quiz. Continuation of the discussion of Chapter 4.
Physics 141, Lecture 7. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 07, Page 1 Outline. Course information: Homework set # 3 Exam # 1 Quiz. Continuation of the
More informationKEELE UNIVERSITY PHYSICS/ASTROPHYSICS MODULE PHY OSCILLATIONS AND WAVES PRACTICE EXAM
KEELE UNIVERSITY PHYSICS/ASTROPHYSICS MODULE PHY-10012 OSCILLATIONS AND WAVES PRACTICE EXAM Candidates should attempt ALL of PARTS A and B, and TWO questions from PART C. PARTS A and B should be answered
More informationRutgers University Department of Physics & Astronomy. 01:750:271 Honors Physics I Fall Lecture 20 JJ II. Home Page. Title Page.
Rutgers University Department of Physics & Astronomy 01:750:271 Honors Physics Fall 2015 Lecture 20 Page 1 of 31 1. No quizzes during Thanksgiving week. There will be recitation according to the regular
More informationHarmonic Oscillator. Mass-Spring Oscillator Resonance The Pendulum. Physics 109 Experiment Number 12
Harmonic Oscillator Mass-Spring Oscillator Resonance The Pendulum Physics 109 Experiment Number 12 Outline Simple harmonic motion The vertical mass-spring system Driven oscillations and resonance The pendulum
More informationUniversity Physics 226N/231N Old Dominion University. Chapter 14: Oscillatory Motion
University Physics 226N/231N Old Dominion University Chapter 14: Oscillatory Motion Dr. Todd Satogata (ODU/Jefferson Lab) satogata@jlab.org http://www.toddsatogata.net/2016-odu Monday, November 5, 2016
More informationSimple Harmonic Motion Test Tuesday 11/7
Simple Harmonic Motion Test Tuesday 11/7 Chapter 11 Vibrations and Waves 1 If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is
More informationProblem 1: Lagrangians and Conserved Quantities. Consider the following action for a particle of mass m moving in one dimension
105A Practice Final Solutions March 13, 01 William Kelly Problem 1: Lagrangians and Conserved Quantities Consider the following action for a particle of mass m moving in one dimension S = dtl = mc dt 1
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 informationCHAPTER 7: OSCILLATORY MOTION REQUIRES A SET OF CONDITIONS
CHAPTER 7: OSCILLATORY MOTION REQUIRES A SET OF CONDITIONS 7.1 Period and Frequency Anything that vibrates or repeats its motion regularly is said to have oscillatory motion (sometimes called harmonic
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 informationChap. 15: Simple Harmonic Motion
Chap. 15: Simple Harmonic Motion Announcements: CAPA is due next Tuesday and next Friday. Web page: http://www.colorado.edu/physics/phys1110/phys1110_sp12/ Examples of periodic motion vibrating guitar
More informationPhysics 101 Discussion Week 12 Explanation (2011)
Physics 101 Discussion Week 12 Eplanation (2011) D12-1 Horizontal oscillation Q0. This is obviously about a harmonic oscillator. Can you write down Newton s second law in the (horizontal) direction? Let
More informationAP Physics. Harmonic Motion. Multiple Choice. Test E
AP Physics Harmonic Motion Multiple Choice Test E A 0.10-Kg block is attached to a spring, initially unstretched, of force constant k = 40 N m as shown below. The block is released from rest at t = 0 sec.
More informationOscillatory Motion and Wave Motion
Oscillatory Motion and Wave Motion Oscillatory Motion Simple Harmonic Motion Wave Motion Waves Motion of an Object Attached to a Spring The Pendulum Transverse and Longitudinal Waves Sinusoidal Wave Function
More information11/17/10. Chapter 14. Oscillations. Chapter 14. Oscillations Topics: Simple Harmonic Motion. Simple Harmonic Motion
11/17/10 Chapter 14. Oscillations This striking computergenerated image demonstrates an important type of motion: oscillatory motion. Examples of oscillatory motion include a car bouncing up and down,
More informationPHYSICS. Chapter 15 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 15 Lecture RANDALL D. KNIGHT Chapter 15 Oscillations IN THIS CHAPTER, you will learn about systems that oscillate in simple harmonic
More informationChapter 14 Oscillations
Chapter 14 Oscillations Chapter Goal: To understand systems that oscillate with simple harmonic motion. Slide 14-2 Chapter 14 Preview Slide 14-3 Chapter 14 Preview Slide 14-4 Chapter 14 Preview Slide 14-5
More informationThe object of this experiment is to study systems undergoing simple harmonic motion.
Chapter 9 Simple Harmonic Motion 9.1 Purpose The object of this experiment is to study systems undergoing simple harmonic motion. 9.2 Introduction This experiment will develop your ability to perform calculations
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 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 informationC. points X and Y only. D. points O, X and Y only. (Total 1 mark)
Grade 11 Physics -- Homework 16 -- Answers on a separate sheet of paper, please 1. A cart, connected to two identical springs, is oscillating with simple harmonic motion between two points X and Y that
More informationThe Harmonic Oscillator
The Harmonic Oscillator Math 4: Ordinary Differential Equations Chris Meyer May 3, 008 Introduction The harmonic oscillator is a common model used in physics because of the wide range of problems it can
More informationPHYSICS 149: Lecture 22
PHYSICS 149: Lecture 22 Chapter 11: Waves 11.1 Waves and Energy Transport 11.2 Transverse and Longitudinal Waves 11.3 Speed of Transverse Waves on a String 11.4 Periodic Waves Lecture 22 Purdue University,
More informationWave Motion: v=λf [m/s=m 1/s] Example 1: A person on a pier observes a set of incoming waves that have a sinusoidal form with a distance of 1.
Wave Motion: v=λf [m/s=m 1/s] Example 1: A person on a pier observes a set of incoming waves that have a sinusoidal form with a distance of 1.6 m between the crests. If a wave laps against the pier every
More informationChapter 14 Oscillations. Copyright 2009 Pearson Education, Inc.
Chapter 14 Oscillations 14-1 Oscillations of a Spring If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The
More informationChapter 7 Hooke s Force law and Simple Harmonic Oscillations
Chapter 7 Hooke s Force law and Simple Harmonic Oscillations Hooke s Law An empirically derived relationship that approximately works for many materials over a limited range. Exactly true for a massless,
More informationHarmonic Oscillator. Outline. Oscillatory Motion or Simple Harmonic Motion. Oscillatory Motion or Simple Harmonic Motion
Harmonic Oscillator Mass-Spring Oscillator Resonance The Pendulum Physics 109, Class Period 13 Experiment Number 11 in the Physics 121 Lab Manual (page 65) Outline Simple harmonic motion The vertical mass-spring
More informationFaculty of Computers and Information. Basic Science Department
18--018 FCI 1 Faculty of Computers and Information Basic Science Department 017-018 Prof. Nabila.M.Hassan 18--018 FCI Aims of Course: The graduates have to know the nature of vibration wave motions with
More informationChapter 13. Hooke s Law: F = - kx Periodic & Simple Harmonic Motion Springs & Pendula Waves Superposition. Next Week!
Chapter 13 Hooke s Law: F = - kx Periodic & Simple Harmonic Motion Springs & Pendula Waves Superposition Next Week! Review Physics 2A: Springs, Pendula & Circular Motion Elastic Systems F = kx Small Vibrations
More informationChapter 12. Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = -kx
Chapter 1 Lecture Notes Chapter 1 Oscillatory Motion Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = -kx When the mass is released, the spring will pull
More informationExam Question 6/8 (HL/OL): Circular and Simple Harmonic Motion. February 1, Applied Mathematics: Lecture 7. Brendan Williamson.
in a : Exam Question 6/8 (HL/OL): Circular and February 1, 2017 in a This lecture pertains to material relevant to question 6 of the paper, and question 8 of the Ordinary Level paper, commonly referred
More informationCopyright 2009, August E. Evrard.
Unless otherwise noted, the content of this course material is licensed under a Creative Commons BY 3.0 License. http://creativecommons.org/licenses/by/3.0/ Copyright 2009, August E. Evrard. You assume
More informationLab 10: Harmonic Motion and the Pendulum
Lab 10 Harmonic Motion and the Pendulum 119 Name Date Partners Lab 10: Harmonic Motion and the Pendulum OVERVIEW A body is said to be in a position of stable equilibrium if, after displacement in any direction,
More informationChapter 14. Oscillations. Oscillations Introductory Terminology Simple Harmonic Motion:
Chapter 14 Oscillations Oscillations Introductory Terminology Simple Harmonic Motion: Kinematics Energy Examples of Simple Harmonic Oscillators Damped and Forced Oscillations. Resonance. Periodic Motion
More informationChapter 14 Oscillations
Chapter 14 Oscillations If an object vibrates or oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The mass and spring system is a
More informationCHAPTER 12 OSCILLATORY MOTION
CHAPTER 1 OSCILLATORY MOTION Before starting the discussion of the chapter s concepts it is worth to define some terms we will use frequently in this chapter: 1. The period of the motion, T, is the time
More informationOscillations. Simple Harmonic Motion (SHM) Position, Velocity, Acceleration SHM Forces SHM Energy Period of oscillation Damping and Resonance
Oscillations Simple Harmonic Motion (SHM) Position, Velocity, Acceleration SHM Forces SHM Energy Period of oscillation Damping and Resonance 1 Revision problem Please try problem #31 on page 480 A pendulum
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 informationChapter 13 Oscillations about Equilibrium. Copyright 2010 Pearson Education, Inc.
Chapter 13 Oscillations about Equilibrium Periodic Motion Units of Chapter 13 Simple Harmonic Motion Connections between Uniform Circular Motion and Simple Harmonic Motion The Period of a Mass on a Spring
More informationOscillator Homework Problems
Oscillator Homework Problems Michael Fowler 3//7 1 Dimensional exercises: use dimensions to find a characteristic time for an undamped simple harmonic oscillator, and a pendulum Why does the dimensional
More informationEF 152 Exam 2 - Spring, 2017 Page 1 Copy 223
EF 152 Exam 2 - Spring, 2017 Page 1 Copy 223 Instructions Do not open the exam until instructed to do so. Do not leave if there is less than 5 minutes to go in the exam. When time is called, immediately
More informationTraveling Waves: Energy Transport
Traveling Waves: Energ Transport wave is a traveling disturbance that transports energ but not matter. Intensit: I P power rea Intensit I power per unit area (measured in Watts/m 2 ) Intensit is proportional
More informationPhysics 2310 Lab #3 Driven Harmonic Oscillator
Physics 2310 Lab #3 Driven Harmonic Oscillator M. Pierce (adapted from a lab by the UCLA Physics & Astronomy Department) Objective: The objective of this experiment is to characterize the behavior of a
More informationMechanics Oscillations Simple Harmonic Motion
Mechanics Oscillations Simple Harmonic Motion Lana Sheridan De Anza College Dec 3, 2018 Last time gravity Newton s universal law of gravitation gravitational field gravitational potential energy Overview
More informationChapter 4. Oscillatory Motion. 4.1 The Important Stuff Simple Harmonic Motion
Chapter 4 Oscillatory Motion 4.1 The Important Stuff 4.1.1 Simple Harmonic Motion In this chapter we consider systems which have a motion which repeats itself in time, that is, it is periodic. In particular
More informationChapter 10 Lecture Outline. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Chapter 10 Lecture Outline Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Chapter 10: Elasticity and Oscillations Elastic Deformations Hooke s Law Stress and
More informationLectures Chapter 10 (Cutnell & Johnson, Physics 7 th edition)
PH 201-4A spring 2007 Simple Harmonic Motion Lectures 24-25 Chapter 10 (Cutnell & Johnson, Physics 7 th edition) 1 The Ideal Spring Springs are objects that exhibit elastic behavior. It will return back
More informationWAVES & SIMPLE HARMONIC MOTION
PROJECT WAVES & SIMPLE HARMONIC MOTION EVERY WAVE, REGARDLESS OF HOW HIGH AND FORCEFUL IT CRESTS, MUST EVENTUALLY COLLAPSE WITHIN ITSELF. - STEFAN ZWEIG What s a Wave? A wave is a wiggle in time and space
More informationClassical Mechanics Phys105A, Winter 2007
Classical Mechanics Phys5A, Winter 7 Wim van Dam Room 59, Harold Frank Hall vandam@cs.ucsb.edu http://www.cs.ucsb.edu/~vandam/ Phys5A, Winter 7, Wim van Dam, UCSB Midterm New homework has been announced
More informationA Level. A Level Physics. Oscillations (Answers) AQA, Edexcel. Name: Total Marks: /30
Visit http://www.mathsmadeeasy.co.uk/ for more fantastic resources. AQA, Edexcel A Level A Level Physics Oscillations (Answers) Name: Total Marks: /30 Maths Made Easy Complete Tuition Ltd 2017 1. The graph
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 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 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 informationLinear and Nonlinear Oscillators (Lecture 2)
Linear and Nonlinear Oscillators (Lecture 2) January 25, 2016 7/441 Lecture outline A simple model of a linear oscillator lies in the foundation of many physical phenomena in accelerator dynamics. A typical
More informationPhysics 132 3/31/17. March 31, 2017 Physics 132 Prof. E. F. Redish Theme Music: Benny Goodman. Swing, Swing, Swing. Cartoon: Bill Watterson
March 31, 2017 Physics 132 Prof. E. F. Redish Theme Music: Benny Goodman Swing, Swing, Swing Cartoon: Bill Watterson Calvin & Hobbes 1 Outline The makeup exam Recap: the math of the harmonic oscillator
More information1) SIMPLE HARMONIC MOTION/OSCILLATIONS
1) SIMPLE HARMONIC MOTION/OSCILLATIONS 1.1) OSCILLATIONS Introduction: - An event or motion that repeats itself at regular intervals is said to be periodic. Periodicity in Space is the regular appearance
More informationFinal Review, Day 1. Announcements: Web page:
Announcements: Final Review, Day 1 Final exam next Wednesday (5/9) at 7:30am in the Coors Event Center. Recitation tomorrow is a review. Please feel free to ask the TA any questions on the course material.
More informationPhysics 231. Topic 7: Oscillations. Alex Brown October MSU Physics 231 Fall
Physics 231 Topic 7: Oscillations Alex Brown October 14-19 2015 MSU Physics 231 Fall 2015 1 Key Concepts: Springs and Oscillations Springs Periodic Motion Frequency & Period Simple Harmonic Motion (SHM)
More informationChap 11. Vibration and Waves. The impressed force on an object is proportional to its displacement from it equilibrium position.
Chap 11. Vibration and Waves Sec. 11.1 - Simple Harmonic Motion The impressed force on an object is proportional to its displacement from it equilibrium position. F x This restoring force opposes the change
More informationEnergy in Planetary Orbits
Lecture 19: Energy in Orbits, Bohr Atom, Oscillatory Motion 1 Energy in Planetary Orbits Consequences of Kepler s First and Third Laws According to Kepler s First Law of Planetary Motion, all planets move
More informationPhysics Mechanics. Lecture 32 Oscillations II
Physics 170 - Mechanics Lecture 32 Oscillations II Gravitational Potential Energy A plot of the gravitational potential energy U g looks like this: Energy Conservation Total mechanical energy of an object
More informationDamped Oscillation Solution
Lecture 19 (Chapter 7): Energy Damping, s 1 OverDamped Oscillation Solution Damped Oscillation Solution The last case has β 2 ω 2 0 > 0. In this case we define another real frequency ω 2 = β 2 ω 2 0. In
More information4.1 KINEMATICS OF SIMPLE HARMONIC MOTION 4.2 ENERGY CHANGES DURING SIMPLE HARMONIC MOTION 4.3 FORCED OSCILLATIONS AND RESONANCE Notes
4.1 KINEMATICS OF SIMPLE HARMONIC MOTION 4.2 ENERGY CHANGES DURING SIMPLE HARMONIC MOTION 4.3 FORCED OSCILLATIONS AND RESONANCE Notes I. DEFINING TERMS A. HOW ARE OSCILLATIONS RELATED TO WAVES? II. EQUATIONS
More information8. What is the period of a pendulum consisting of a 6-kg object oscillating on a 4-m string?
1. In the produce section of a supermarket, five pears are placed on a spring scale. The placement of the pears stretches the spring and causes the dial to move from zero to a reading of 2.0 kg. If the
More informationPhysics 231 Lecture 18
Physics 31 ecture 18 τ = Fd;d is the lever arm Main points of today s lecture: Energy Pendulum T = π g ( ) θ = θmax cos πft + ϑ0 Damped Oscillations x x equibrium = Ae bt/(m) cos(ω damped t) ω damped =
More informationOscillations Simple Harmonic Motion
Oscillations Simple Harmonic Motion Lana Sheridan De Anza College Dec 1, 2017 Overview oscillations simple harmonic motion (SHM) spring systems energy in SHM pendula damped oscillations Oscillations and
More informationChapter 14. PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman. Lectures by Wayne Anderson
Chapter 14 Periodic Motion PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 14 To describe oscillations in
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 informationOscillation the vibration of an object. Wave a transfer of energy without a transfer of matter
Oscillation the vibration of an object Wave a transfer of energy without a transfer of matter Equilibrium Position position of object at rest (mean position) Displacement (x) distance in a particular direction
More informationEnergy in a Simple Harmonic Oscillator. Class 30. Simple Harmonic Motion
Simple Harmonic Motion Class 30 Here is a simulation of a mass hanging from a spring. This is a case of stable equilibrium in which there is a large extension in which the restoring force is linear in
More informationOscillations and Waves
Oscillations and Waves Oscillation: Wave: Examples of oscillations: 1. mass on spring (eg. bungee jumping) 2. pendulum (eg. swing) 3. object bobbing in water (eg. buoy, boat) 4. vibrating cantilever (eg.
More informationFundamentals Physics. Chapter 15 Oscillations
Fundamentals Physics Tenth Edition Halliday Chapter 15 Oscillations 15-1 Simple Harmonic Motion (1 of 20) Learning Objectives 15.01 Distinguish simple harmonic motion from other types of periodic motion.
More informationChapter 15. Oscillatory Motion
Chapter 15 Oscillatory Motion Part 2 Oscillations and Mechanical Waves Periodic motion is the repeating motion of an object in which it continues to return to a given position after a fixed time interval.
More informationA B = AB cos θ = 100. = 6t. a(t) = d2 r(t) a(t = 2) = 12 ĵ
1. A ball is thrown vertically upward from the Earth s surface and falls back to Earth. Which of the graphs below best symbolizes its speed v(t) as a function of time, neglecting air resistance: The answer
More information!T = 2# T = 2! " The velocity and acceleration of the object are found by taking the first and second derivative of the position:
A pendulum swinging back and forth or a mass oscillating on a spring are two examples of (SHM.) SHM occurs any time the position of an object as a function of time can be represented by a sine wave. We
More informationPHY217: Vibrations and Waves
Assessed Problem set 1 Issued: 5 November 01 PHY17: Vibrations and Waves Deadline for submission: 5 pm Thursday 15th November, to the V&W pigeon hole in the Physics reception on the 1st floor of the GO
More informationPhysics 41 HW Set 1 Chapter 15 Serway 8 th ( 7 th )
Conceptual Q: 4 (7), 7 (), 8 (6) Physics 4 HW Set Chapter 5 Serway 8 th ( 7 th ) Q4(7) Answer (c). The equilibrium position is 5 cm below the starting point. The motion is symmetric about the equilibrium
More informationPhysics 351, Spring 2017, Homework #3. Due at start of class, Friday, February 3, 2017
Physics 351, Spring 2017, Homework #3. Due at start of class, Friday, February 3, 2017 Course info is at positron.hep.upenn.edu/p351 When you finish this homework, remember to visit the feedback page at
More informationBSc/MSci MidTerm Test
BSc/MSci MidTerm Test PHY-217 Vibrations and Waves Time Allowed: 40 minutes Date: 18 th Nov, 2011 Time: 9:10-9:50 Instructions: Answer ALL questions in section A. Answer ONLY ONE questions from section
More informationGeneral Physics (PHY 2130)
General Physics (PHY 2130) Lecture 25 Oscillations simple harmonic motion pendulum driven and damped oscillations http://www.physics.wayne.edu/~apetrov/phy2130/ Lightning Review Last lecture: 1. Oscillations
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 information本教材僅供教學使用, 勿做其他用途, 以維護智慧財產權
本教材內容主要取自課本 Physics for Scientists and Engineers with Modern Physics 7th Edition. Jewett & Serway. 注意 本教材僅供教學使用, 勿做其他用途, 以維護智慧財產權 教材網址 : https://sites.google.com/site/ndhugp1 1 Chapter 15 Oscillatory Motion
More informationChapter 13 Lecture. Essential University Physics Richard Wolfson 2 nd Edition. Oscillatory Motion Pearson Education, Inc.
Chapter 13 Lecture Essential University Physics Richard Wolfson nd Edition Oscillatory Motion Slide 13-1 In this lecture you ll learn To describe the conditions under which oscillatory motion occurs To
More informationWelcome back to Physics 215. Review gravity Oscillations Simple harmonic motion
Welcome back to Physics 215 Review gravity Oscillations Simple harmonic motion Physics 215 Spring 2018 Lecture 14-1 1 Final Exam: Friday May 4 th 5:15-7:15pm Exam will be 2 hours long Have an exam buddy
More informationAnswers to examination-style questions. Answers Marks Examiner s tips
(a) (i) With the object on the spring: the mean value of x = 72 mm, e = 70 mm (ii).4% Each reading was ±0.5 mm. As the extension was the subtraction of two readings the absolute errors are added to give
More informationDON T PANIC! If you get stuck, take a deep breath and go on to the next question. Come back to the question you left if you have time at the end.
Math 307, Midterm 2 Winter 2013 Name: Instructions. DON T PANIC! If you get stuck, take a deep breath and go on to the next question. Come back to the question you left if you have time at the end. There
More informationPhysics 6B. Practice Midterm #1 Solutions
Physics 6B Practice Midterm #1 Solutions 1. A block of plastic with a density of 90 kg/m 3 floats at the interface between of density 850 kg/m 3 and of density 1000 kg/m 3, as shown. Calculate the percentage
More informationAP Physics C 2015 Summer Assignment
AP Physics C 2015 Summer Assignment College Board (the people in charge of AP exams) recommends students to only take AP Physics C if they have already taken a 1 st year physics course and are currently
More informationLAB #6 The Swaying Building
LAB #6 The Swaying Building Goal: Determine a model of the swaying of a skyscraper; estimating parameters Required tools: Matlab routines pplane, ode45, plot; M-files; systems of differential equations.
More informationOSCILLATIONS ABOUT EQUILIBRIUM
OSCILLATIONS ABOUT EQUILIBRIUM Chapter 13 Units of Chapter 13 Periodic Motion Simple Harmonic Motion Connections between Uniform Circular Motion and Simple Harmonic Motion The Period of a Mass on a Spring
More information