Chapter 15 - Oscillations
|
|
- Debra Garrison
- 6 years ago
- Views:
Transcription
1 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
2 Oscillatory motion is motion that is periodic in time (e.g., earthquake shakes, guitar strings).
3 Oscillatory motion is motion that is periodic in time (e.g., earthquake shakes, guitar strings). The period T measures the time for one oscillation.
4 Oscillatory motion that is sinusoidal is known as Motion. x(t) = x m cos(ωt)
5 Oscillatory motion that is sinusoidal is known as Motion. x(t) = x m cos(ωt) x m is the maximum displacement
6 Oscillatory motion that is sinusoidal is known as Motion. x(t) = x m cos(ωt) x m is the maximum displacement ω is the angular frequency: ω = 2πf = 2π/T.
7 Two oscillators can have different frequencies, or different phases: x(t) = x m cos(ωt + φ)
8 Sinusoidal oscillations are described by these definitions: x(t) = x m cos(ωt + φ) T = 1/f ω = 2πf
9 Sinusoidal oscillations are described by these definitions: x(t) = x m cos(ωt + φ) T = 1/f ω = 2πf x in meters T in seconds f in Hertz (1/s) ω in rad/s
10 Since we know the position of an oscillating object, we also know its velocity and acceleration: x(t) = x m cos(ωt + φ) v(t) = dx dt = ωx m sin(ωt + φ) a(t) = dv dt = ω2 x m cos(ωt + φ)
11 The maximum velocity and acceleration depend on the frequency and the maximum displacement. Max position: x m Max velocity: ωx m Max acceleration: ω 2 x m
12 Simple harmonic motion is generated by a linear restoring force: F = kx = ma = m d2 x dt 2
13 Simple harmonic motion is generated by a linear restoring force: F = kx = ma = m d2 x dt 2 d 2 x dt 2 + k m x = 0
14 Simple harmonic motion is generated by a linear restoring force: F = kx = ma = m d2 x dt 2 d 2 x dt 2 + k m x = 0 The solution to this differential equation: (so ω = k/m) x(t) = x m cos( k/mt + φ)
15 The motion of a SHO is related to motion in a circle. x(t) = x m cos(ωt + φ)
16 The motion of a SHO is related to motion in a circle. x(t) = x m cos(ωt + φ) v(t) = ωx m sin(ωt + φ)
17 The motion of a SHO is related to motion in a circle. x(t) = x m cos(ωt + φ) v(t) = ωx m sin(ωt + φ) a(t) = ω 2 x m cos(ωt + φ)
18 Chapter 15 Lecture Question 15.1 The graph below represents the oscillatory motion of three different springs with identical masses attached to each. Which of these springs has the smallest spring constant? (a) Graph 1 (b) Graph 2 (c) Graph 3 (d) Both 2 and 3 are smallest and equal (e) All three have the same spring constant.
19 A spring stores potential energy. To find it, calculate the work the spring force does: U = W = x2 x 1 ( kx)dx = 1 2 kx kx2 1
20 A spring stores potential energy. To find it, calculate the work the spring force does: x2 U = W = ( kx)dx = 1 x 1 2 kx kx2 1 A spring compressed by x stores energy U = 1 2 kx2.
21 As a mass oscillates, the energy transfers from kinetic to potential energy.
22 As a mass oscillates, the energy transfers from kinetic to potential energy. At the ends of the motion, velocity is zero, K is zero and U is maximum.
23
24 The energy oscillates between: U = 1 2 kx2 = 1 2 kx2 m cos 2 (ωt + φ) K = 1 2 mv2 = 1 2 }{{} mω2 xm 2 sin 2 (ωt + φ) k
25 The energy oscillates between: U = 1 2 kx2 = 1 2 kx2 m cos 2 (ωt + φ) K = 1 2 mv2 = 1 2 }{{} mω2 xm 2 sin 2 (ωt + φ) k E = U + K = U = 1 2 kx2 m
26 A simple pendulum is a ball on a string. It acts like a SHO for small angles. The restoring force: F = mg sin θ mgθ I = ml 2
27 For small angles (θ < 20 ), a pendulum is like a simple harmonic oscillator. τ = (mgθ)l = Iα = I d2 θ dt 2
28 For small angles (θ < 20 ), a pendulum is like a simple harmonic oscillator. τ = (mgθ)l = Iα = I d2 θ dt 2 d 2 θ dt 2 + mgl θ }{{} I = 0 ω 2
29 For small angles (θ < 20 ), a pendulum is like a simple harmonic oscillator. τ = (mgθ)l = Iα = I d2 θ dt 2 d 2 θ dt 2 + mgl θ }{{} I = 0 ω 2 θ(t) = θ m cos(ωt + φ)
30 For small angles (θ < 20 ), a pendulum is like a simple harmonic oscillator. τ = (mgθ)l = Iα = I d2 θ dt 2 d 2 θ dt 2 + mgl θ }{{} I = 0 ω 2 θ(t) = θ m cos(ωt + φ) ω = mgl/i = g/l
31 For small angles (θ < 20 ), a pendulum is like a simple harmonic oscillator. τ = (mgθ)l = Iα = I d2 θ dt 2 d 2 θ dt 2 + mgl θ }{{} I = 0 ω 2 θ(t) = θ m cos(ωt + φ) ω = mgl/i = g/l T = 1/f = 2π/ω = 2π L/g
32 For a physical pendulum with moment of inertia I and small oscillations,
33 For a physical pendulum with moment of inertia I and small oscillations, d 2 θ dt 2 + mgh θ = 0 I
34 For a physical pendulum with moment of inertia I and small oscillations, d 2 θ dt 2 + mgh θ = 0 I ω = mgh/i
35 For a physical pendulum with moment of inertia I and small oscillations, d 2 θ dt 2 + mgh θ = 0 I ω = mgh/i T = 1/f = 2π/ω = 2π I/mgh
36 A torsion pendulum is a symmetric object where the restoring torque arises from a twisted wire. τ = κθ (similar to spring)
37 A torsion pendulum is a symmetric object where the restoring torque arises from a twisted wire. τ = κθ (similar to spring) d 2 θ dt 2 + κ I θ = 0
38 A torsion pendulum is a symmetric object where the restoring torque arises from a twisted wire. τ = κθ (similar to spring) d 2 θ dt 2 + κ I θ = 0 ω = κ/i
39 A torsion pendulum is a symmetric object where the restoring torque arises from a twisted wire. τ = κθ (similar to spring) d 2 θ dt 2 + κ I θ = 0 ω = κ/i T = 1/f = 2π/ω = 2π I/κ
40 Chapter 15 Lecture Question 15.3 A grandfather clock, which uses a pendulum to keep accurate time, is adjusted at sea level. The clock is then taken to an altitude of several kilometers. How will the clock behave in its new location? (a) The clock will run slow. (b) The clock will run fast. (c) The clock will run the same as it did at sea level. (d) The clock cannot run at such high altitudes.
41 Damped simple harmonic motion is the result of oscillatory behavior in the presence of a retarding force. with b the damping constant. F d = bv
42 Applying Newton s Second Law to this situation, F net = ma kx bv = ma 0 = d2 x dt 2 + b dx m dt + k m x
43 Applying Newton s Second Law to this situation, F net = ma kx bv = ma 0 = d2 x dt 2 + b dx m dt + k m x The solution: x(t) = x m e bt/2m cos(ω t + φ) k ω = m b2 4m 2
44 For damped harmonic motion, the oscillations will die out over time.
45 For damped harmonic motion, the oscillations will die out over time. Side note: ω k = m b2 is only valid if k/m > b 2 /4m 2. 4m 2 What happens if k/m b 2 /4m 2?
46 If an oscillator of angular frequency ω is driven by an external force at a frequency ω d, then the response will also be at ω d.
47 If an oscillator of angular frequency ω is driven by an external force at a frequency ω d, then the response will also be at ω d. d 2 x dt 2 + k m x = F 0 cos(ωt) x(t) = A cos(ωt + φ)
48 If an oscillator of angular frequency ω is driven by an external force at a frequency ω d, then the response will also be at ω d. d 2 x dt 2 + k m x = F 0 cos(ωt) x(t) = A cos(ωt + φ) The amplitude A depends on the relationship between ω d and ω.
49 If a damped oscillator is driven at its natural frequency, the system is on resonance and the oscillations are maximum.
50 If a damped oscillator is driven at its natural frequency, the system is on resonance and the oscillations are maximum. The width of the resonance peak depends on the damping constant.
Chapter 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 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 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 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 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 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 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. 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 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 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 informationPhysics 2101 S c e t c i cti n o 3 n 3 March 31st Announcements: Quiz today about Ch. 14 Class Website:
Physics 2101 Section 3 March 31 st Announcements: Quiz today about Ch. 14 Class Website: http://www.phys.lsu.edu/classes/spring2010/phys2101 3/ http://www.phys.lsu.edu/~jzhang/teaching.html Simple Harmonic
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 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 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 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 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 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 informationOSCILLATIONS.
OSCILLATIONS Periodic Motion and Oscillatory motion If a body repeats its motion along a certain path, about a fixed point, at a definite interval of time, it is said to have a periodic motion If a body
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 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 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 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 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 informationOscillations and Waves
Oscillations and Waves Somnath Bharadwaj and S. Pratik Khastgir Department of Physics and Meteorology IIT Kharagpur Module : Oscillations Lecture : Oscillations Oscillations are ubiquitous. It would be
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 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 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 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 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 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 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 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 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 informationLecture 18. In other words, if you double the stress, you double the resulting strain.
Lecture 18 Stress and Strain and Springs Simple Harmonic Motion Cutnell+Johnson: 10.1-10.4,10.7-10.8 Stress and Strain and Springs So far we ve dealt with rigid objects. A rigid object doesn t change shape
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 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 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 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 information15 OSCILLATIONS. Introduction. Chapter Outline Simple Harmonic Motion 15.2 Energy in Simple Harmonic Motion
Chapter 15 Oscillations 761 15 OSCILLATIONS Figure 15.1 (a) The Comcast Building in Philadelphia, Pennsylvania, looming high above the skyline, is approximately 305 meters (1000 feet) tall. At this height,
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. 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 Exam 3 results Class Average - 57 (Approximate grade
More informationThe distance of the object from the equilibrium position is m.
Answers, Even-Numbered Problems, Chapter..4.6.8.0..4.6.8 (a) A = 0.0 m (b).60 s (c) 0.65 Hz Whenever the object is released from rest, its initial displacement equals the amplitude of its SHM. (a) so 0.065
More informationChapter 13 Solutions
Chapter 3 Solutions 3. x = (4.00 m) cos (3.00πt + π) Compare this with x = A cos (ωt + φ) to find (a) ω = πf = 3.00π or f =.50 Hz T = f = 0.667 s A = 4.00 m (c) φ = π rad (d) x(t = 0.50 s) = (4.00 m) cos
More informationOscillations. Phys101 Lectures 28, 29. Key points: Simple Harmonic Motion (SHM) SHM Related to Uniform Circular Motion The Simple Pendulum
Phys101 Lectures 8, 9 Oscillations Key points: Simple Harmonic Motion (SHM) SHM Related to Uniform Circular Motion The Simple Pendulum Ref: 11-1,,3,4. Page 1 Oscillations of a Spring If an object oscillates
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 informationUnforced Oscillations
Unforced Oscillations Simple Harmonic Motion Hooke s Law Newton s Second Law Method of Force Competition Visualization of Harmonic Motion Phase-Amplitude Conversion The Simple Pendulum and The Linearized
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 informationAP Pd 3 Rotational Dynamics.notebook. May 08, 2014
1 Rotational Dynamics Why do objects spin? Objects can travel in different ways: Translation all points on the body travel in parallel paths Rotation all points on the body move around a fixed point An
More informationChapter 14 (Oscillations) Key concept: Downloaded from
Chapter 14 (Oscillations) Multiple Choice Questions Single Correct Answer Type Q1. The displacement of a particle is represented by the equation. The motion of the particle is (a) simple harmonic with
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 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 informationE = K + U. p mv. p i = p f. F dt = p. J t 1. a r = v2. F c = m v2. s = rθ. a t = rα. r 2 dm i. m i r 2 i. I ring = MR 2.
v = v i + at x = x i + v i t + 1 2 at2 E = K + U p mv p i = p f L r p = Iω τ r F = rf sin θ v 2 = v 2 i + 2a x F = ma = dp dt = U v dx dt a dv dt = d2 x dt 2 A circle = πr 2 A sphere = 4πr 2 V sphere =
More informationSlide 1 / 70. Simple Harmonic Motion
Slide 1 / 70 Simple Harmonic Motion Slide 2 / 70 SHM and Circular Motion There is a deep connection between Simple Harmonic Motion (SHM) and Uniform Circular Motion (UCM). Simple Harmonic Motion can be
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 informationDouble Spring Harmonic Oscillator Lab
Dylan Humenik and Benjamin Daily Double Spring Harmonic Oscillator Lab Objectives: -Experimentally determine harmonic equations for a double spring system using various methods Part 1 Determining k of
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 informationVibrations and Waves MP205, Assignment 4 Solutions
Vibrations and Waves MP205, Assignment Solutions 1. Verify that x = Ae αt cos ωt is a possible solution of the equation and find α and ω in terms of γ and ω 0. [20] dt 2 + γ dx dt + ω2 0x = 0, Given x
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 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 informationOscillations. Tacoma Narrow Bridge: Example of Torsional Oscillation
Oscillations Mechanical Mass-spring system nd order differential eq. Energy tossing between mass (kinetic energy) and spring (potential energy) Effect of friction, critical damping (shock absorber) Simple
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 informationEssential Physics I. Lecture 9:
Essential Physics I E I Lecture 9: 15-06-15 Last lecture: review Conservation of momentum: p = m v p before = p after m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f m 1 m 1 m 2 m 2 Elastic collision: +
More informationPhysics 101 Lecture 18 Vibrations, SHM, Waves (II)
Physics 101 Lecture 18 Vibrations, SHM, Waves (II) Reminder: simple harmonic motion is the result if we have a restoring force that is linear with the displacement: F = -k x What would happen if you could
More informationOscillatory Motion. Solutions of Selected Problems
Chapter 15 Oscillatory Motion. Solutions of Selected Problems 15.1 Problem 15.18 (In the text book) A block-spring system oscillates with an amplitude of 3.50 cm. If the spring constant is 250 N/m and
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 informationImportant because SHM is a good model to describe vibrations of a guitar string, vibrations of atoms in molecules, etc.
Simple Harmonic Motion Oscillatory motion under a restoring force proportional to the amount of displacement from equilibrium A restoring force is a force that tries to move the system back to equilibrium
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 informationt = g = 10 m/s 2 = 2 s T = 2π g
Annotated Answers to the 1984 AP Physics C Mechanics Multiple Choice 1. D. Torque is the rotational analogue of force; F net = ma corresponds to τ net = Iα. 2. C. The horizontal speed does not affect the
More informationThursday March 30 Topics for this Lecture: Simple Harmonic Motion Kinetic & Potential Energy Pendulum systems Resonances & Damping.
Thursday March 30 Topics for this Lecture: Simple Harmonic Motion Kinetic & Potential Energy Pendulum systems Resonances & Damping Assignment 11 due Friday Pre-class due 15min before class Help Room: Here,
More information5.6 Unforced Mechanical Vibrations
5.6 Unforced Mechanical Vibrations 215 5.6 Unforced Mechanical Vibrations The study of vibrating mechanical systems begins here with examples for unforced systems with one degree of freedom. The main example
More informationPREMED COURSE, 14/08/2015 OSCILLATIONS
PREMED COURSE, 14/08/2015 OSCILLATIONS PERIODIC MOTIONS Mechanical Metronom Laser Optical Bunjee jumping Electrical Astronomical Pulsar Biological ECG AC 50 Hz Another biological exampe PERIODIC MOTIONS
More informationSimple Harmonic Motion
Pendula Simple Harmonic Motion diff. eq. d 2 y dt 2 =!Ky 1. Know frequency (& period) immediately from diff. eq.! = K 2. Initial conditions: they will be of 2 kinds A. at rest initially y(0) = y o v y
More informationPhysics 8 Monday, December 4, 2017
Physics 8 Monday, December 4, 2017 HW12 due Friday. Grace will do a review session Dec 12 or 13. When? I will do a review session: afternoon Dec 17? Evening Dec 18? Wednesday, I will hand out the practice
More informationCh 15 Simple Harmonic Motion
Ch 15 Simple Harmonic Motion Periodic (Circular) Motion Point P is travelling in a circle with a constant speed. How can we determine the x-coordinate of the point P in terms of other given quantities?
More informationFor more info visit
Types of Motion:- (a) Periodic motion:- When a body or a moving particle repeats its motion along a definite path after regular intervals of time, its motion is said to be Periodic Motion and interval
More informationChapter 16 Waves. Types of waves Mechanical waves. Electromagnetic waves. Matter waves
Chapter 16 Waves Types of waves Mechanical waves exist only within a material medium. e.g. water waves, sound waves, etc. Electromagnetic waves require no material medium to exist. e.g. light, radio, microwaves,
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 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 informationENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 10 NATURAL VIBRATIONS ONE DEGREE OF FREEDOM
ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D5 TUTORIAL 0 NATURAL VIBRATIONS ONE DEGREE OF FREEDOM On completion of this tutorial you should be able to do the following. Explain the meaning of degrees
More informationTraveling Harmonic Waves
Traveling Harmonic Waves 6 January 2016 PHYC 1290 Department of Physics and Atmospheric Science Functional Form for Traveling Waves We can show that traveling waves whose shape does not change with time
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 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 informationTorque and Simple Harmonic Motion
Torque and Simple Harmonic Motion Recall: Fixed Axis Rotation Angle variable Angular velocity Angular acceleration Mass element Radius of orbit Kinematics!! " d# / dt! " d 2 # / dt 2!m i Moment of inertia
More informationIntroductory Physics. Week 2015/05/29
2015/05/29 Part I Summary of week 6 Summary of week 6 We studied the motion of a projectile under uniform gravity, and constrained rectilinear motion, introducing the concept of constraint force. Then
More informationAssessment Schedule 2016 Physics: Demonstrate understanding of mechanical systems (91524)
NCEA Level 3 Physics (91524) 2016 page 1 of 6 Assessment Schedule 2016 Physics: Demonstrate understanding of mechanical systems (91524) Evidence Statement NØ N1 N2 A3 A4 M5 M6 E7 E8 No response; no relevant
More informationSimple Harmonic Motion
Chapter 9 Simple Harmonic Motion In This Chapter: Restoring Force Elastic Potential Energy Simple Harmonic Motion Period and Frequency Displacement, Velocity, and Acceleration Pendulums Restoring Force
More informationGood Vibes: Introduction to Oscillations
Good Vibes: Introduction to Oscillations Description: Several conceptual and qualitative questions related to main characteristics of simple harmonic motion: amplitude, displacement, period, frequency,
More information2.4 Models of Oscillation
2.4 Models of Oscillation In this section we give three examples of oscillating physical systems that can be modeled by the harmonic oscillator equation. Such models are ubiquitous in physics, but are
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 informationSimple and Physical Pendulums Challenge Problem Solutions
Simple and Physical Pendulums Challenge Problem Solutions Problem 1 Solutions: For this problem, the answers to parts a) through d) will rely on an analysis of the pendulum motion. There are two conventional
More informationPhysics 8, Fall 2011, equation sheet work in progress
1 year 3.16 10 7 s Physics 8, Fall 2011, equation sheet work in progress circumference of earth 40 10 6 m speed of light c = 2.9979 10 8 m/s mass of proton or neutron 1 amu ( atomic mass unit ) = 1 1.66
More informationSymmetries 2 - Rotations in Space
Symmetries 2 - Rotations in Space This symmetry is about the isotropy of space, i.e. space is the same in all orientations. Thus, if we continuously rotated an entire system in space, we expect the system
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 informationStatic Equilibrium, Gravitation, Periodic Motion
This test covers static equilibrium, universal gravitation, and simple harmonic motion, with some problems requiring a knowledge of basic calculus. Part I. Multiple Choice 1. 60 A B 10 kg A mass of 10
More informationChapter 5 Oscillatory Motion
Chapter 5 Oscillatory Motion Simple Harmonic Motion An object moves with simple harmonic motion whenever its acceleration is proportional to its displacement from some equilibrium position and is oppositely
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 informationClassical Mechanics Comprehensive Exam Solution
Classical Mechanics Comprehensive Exam Solution January 31, 011, 1:00 pm 5:pm Solve the following six problems. In the following problems, e x, e y, and e z are unit vectors in the x, y, and z directions,
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 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 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 information