Chapter 13. F =!kx. Vibrations and Waves. ! = 2" f = 2" T. Hooke s Law Reviewed. Sinusoidal Oscillation Graphing x vs. t. Phases.
|
|
- Marcia Washington
- 6 years ago
- Views:
Transcription
1 Chapter 13 Vibrations and Waves Hooke s Law Reviewed F =!k When is positive, F is negative ; When at equilibrium (=0, F = 0 ; When is negative, F is positive ; 1 2 Sinusoidal Oscillation Graphing vs. t Pen traces a sine wave A A : amplitude (length, m : period (time, s 3 4 = Acos(!t " # = Acos(2$ ft " # = Acos 2$t ' " # ( * Some Vocabulary f = 1! = 2" f = 2" Phases Phase is related to starting time $ = Acos 2!t " # ' ( $ = Acos 2!(t " t 0 ' ( if # = 2!t 0 f = Frequency! = Angular Frequency = Period A = Amplitude " = phase 90-degrees changes cosine to sine $ cos!t " # ' 2 ( = sin!t 5 6
2 Velocity and Acceleration vs. time Velocity is 90 out of phase with : When is at ma, v is at min... Acceleration is 180 out of phase with a = F/m = - (k/m v a v and a vs. t = Acos!t v = "v ma sin!t a = "a ma cos!t Find v ma with E conservation 1 2 ka2 = 1 2 mv 2 ma v ma = A Find a ma using F=ma!k = ma k m!kacos"t =!ma ma cos"t a ma = A k m 7 8 What is!? Requires calculus. Since d Acos!t = "! Asin!t dt v ma =! A = A k m Formula Summary f = 1! = 2" f = 2"! = k m = Acos(!t " # v = "! Asin(!t " # a = "! 2 A(cos!t " #! = k m 9 10 Eample13.1 An block-spring system oscillates with an amplitude of 3.5 cm. If the spring constant is 250 N/m and the block has a mass of 0.50 kg, determine (a the mechanical energy of the system Eample 13.2 A 36-kg block is attached to a spring of constant k=600 N/m. he block is pulled 3.5 cm away from its equilibrium positions and released from rest at t=0. At t=0.75 seconds, (b the maimum speed of the block a what is the position of the block? a cm (c the maimum acceleration. b what is the velocity of the block? b cm/s a J b m/s c 17.5 m/s
3 Eample 13.3 A 36-kg block is attached to a spring of constant k=600 N/m. he block is pulled 3.5 cm away from its equilibrium position and is pushed so that is has an initial velocity of 5.0 cm/s at t=0. a What is the position of the block at t=0.75 seconds? a cm Eample 13.4a epression, (t = 4 + 2cos[!(t " 3] Where will be in cm if t is in seconds he amplitude of the motion is: a 1 cm b 2 cm c 3 cm d 4 cm e -4 cm Eample 13.4b epression, (t = 4 + 2cos[!(t " 3] Here, will be in cm if t is in seconds he period of the motion is: a 1/3 s b 1/2 s c 1 s d 2 s e 2/# s Eample 13.4c epression, (t = 4 + 2cos[!(t " 3] Here, will be in cm if t is in seconds he frequency of the motion is: a 1/3 Hz b 1/2 Hz c 1 Hz d 2 Hz e # Hz Eample 13.4d epression, (t = 4 + 2cos[!(t " 3] Here, will be in cm if t is in seconds he angular frequency of the motion is: a 1/3 rad/s b 1/2 rad/s c 1 rad/s d 2 rad/s e # rad/s Eample 13.4e epression, (t = 4 + 2cos[!(t " 3] Here, will be in cm if t is in seconds he object will pass through the equilibrium position at the times, t = seconds a, -2, -1, 0, 1, 2 b, -1.5, -0.5, 0.5, 1.5, 2.5, c, -1.5, -1, -0.5, 0, 0.5, 1.0, 1.5, d, -4, -2, 0, 2, 4, e, -2.5, -0.5, 1.5, 3.5, 17 18
4 Simple Pendulum F =!mgsin" sin" = # 2 + L 2 L F #! mg L Looks like Hooke s law (k $ mg/l Simple Pendulum F =!mgsin" sin" = # 2 + L 2 L F #! mg L! = g L " = " ma cos(!t # $ Simple pendulum Pendulum Demo! = g L Frequency independent of mass and amplitude! (for small amplitudes Eample 13.5 A man enters a tall tower, needing to know its height h. He notes that a long pendulum etends from the roof almost to the ground and that its period is 15.5 s. In real systems, friction slows motion Damped Oscillations (a How tall is the tower? a 59.7 m (b If this pendulum is taken to the Moon, where the free-fall acceleration is 1.67 m/s 2, what is the period of the pendulum there? b 37.6 s 23 24
5 RAVELING WAVES Longitudinal (Compression Waves Sound Surface of a liquid Vibration of strings Electromagnetic Radio waves Microwaves Infrared Visible Ultraviolet X-rays Gamma-rays Gravity Sound waves are longitudinal waves 25 Compression and ransverse Waves Demo 26 ransverse Waves Elements move perpendicular to wave motion Elements move parallel to wave motion 27 Snapshot of a ransverse Wave 28 Snapshot of Longitudinal Wave ( y = A cos ' 2! # $ * " wavelength ( y = A cos ' 2! # $ * " y could refer to pressure or density 29 30
6 Moving Wave y = Acos 2! " vt ( " $ ' # * moves to right with velocity v Replace with -vt if wave moves to the right. Replace with +vt if wave should move to left. Moving Wave: Formula Summary + # y = Acos 2! $ "! ft. - ' * 0, / Fiing =0, y = Acos!2" v ' # t! $ ( * f = v!, v = f! v = f! Eample 13.6a A wave traveling in the positive direction has a frequency of f = 25.0 Hz as shown in the figure. he wavelength is: a 5 cm b 9 cm c 10 cm d 18 cm e 20 cm Eample 13.6b A wave traveling in the positive direction has a frequency of f = 25.0 Hz as shown in the figure. he amplitude is: a 5 cm b 9 cm c 10 cm d 18 cm e 20 cm Eample 13.6c A wave traveling in the positive direction has a frequency of f = 25.0 Hz as shown in the figure. he speed of the wave is: a 25 cm/s b 50 cm/s c 100 cm/s d 250 cm/s e 500 cm/s Eample 13.7a Consider the following epression for a pressure wave, where it is assumed that is in cm,t is in seconds and P will be given in N/m 2. What is the amplitude? a 1.5 N/m 2 b 3 N/m 2 c 30 N/m 2 d 60 N/m 2 e 120 N/m 2 P = 60! cos 2 " 3t 35 36
7 Eample 13.7b Consider the following epression for a pressure wave, P = 60! cos 2 " 3t where it is assumed that is in cm,t is in seconds and P will be given in N/m 2. What is the wavelength? a 0.5 cm b 1 cm c 1.5 cm d # cm e 2# cm Eample 13.7c Consider the following epression for a pressure wave, where it is assumed that is in cm,t is in seconds and P will be given in N/m 2. What is the frequency? a 1.5 Hz b 3 Hz c 3/# Hz d 3/(2# Hz e 3#/2 Hz P = 60! cos 2 " 3t Eample 13.7d Consider the following epression for a pressure wave, P = 60! cos 2 " 3t where it is assumed that is in cm,t is in seconds and P will be given in N/m 2. What is the speed of the wave? a 1.5 cm/s b 6 cm/s c 2/3 cm/s d 3#/2 cm/s e 2/# cm/s 39 Eample 13.8 Which of these waves move in the positive direction? 1 y =!21.3" cos( t 2 y =!21.3" cos(3.4! 2.5t 3y =!21.3" cos(! t 4y =!21.3" cos(!3.4! 2.5t 5 y = 21.3" cos( t 6 y = 21.3" cos(3.4! 2.5t 7y = 21.3" cos(! t 8y = 21.3" cos(!3.4! 2.5t a 5 and 6 b 1 and 4 c 5,6,7 and 8 d 1,4,5 and 8 e 2,3,6 and 7 40 Speed of a Wave in a Vibrating String Eample 13.9 v = µ where µ = m L A string is tied tightly between points A and B as a communication device. If one wants to double the wave speed, one could: For different kinds of waves: (e.g. sound Always a square root Numerator related to restoring force Denominator is some sort of mass density a Double the tension b Quadruple the tension c Use a string with half the mass d Use a string with double the mass e Use a string with quadruple the mass 41 42
8 Superposition Principle raveling waves can pass through each other without being altered. Reflection Fied End Reflected wave is inverted y(,t = y 1 (,t + y 2 (,t Reflection Free End Reflected pulse not inverted 45
Physics 1C. Lecture 12C
Physics 1C Lecture 12C Simple Pendulum The simple pendulum is another example of simple harmonic motion. Making a quick force diagram of the situation, we find:! The tension in the string cancels out with
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 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 informationCHAPTER 11 VIBRATIONS AND WAVES
CHAPTER 11 VIBRATIONS AND WAVES http://www.physicsclassroom.com/class/waves/u10l1a.html UNITS Simple Harmonic Motion Energy in the Simple Harmonic Oscillator The Period and Sinusoidal Nature of SHM The
More informationOutline. Hook s law. Mass spring system Simple harmonic motion Travelling waves Waves in string Sound waves
Outline Hook s law. Mass spring system Simple harmonic motion Travelling waves Waves in string Sound waves Hooke s Law Force is directly proportional to the displacement of the object from the equilibrium
More informationRaymond A. Serway Chris Vuille. Chapter Thirteen. Vibrations and Waves
Raymond A. Serway Chris Vuille Chapter Thirteen Vibrations and Waves Periodic Motion and Waves Periodic motion is one of the most important kinds of physical behavior Will include a closer look at Hooke
More information(Total 1 mark) IB Questionbank Physics 1
1. A transverse wave travels from left to right. The diagram below shows how, at a particular instant of time, the displacement of particles in the medium varies with position. Which arrow represents the
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 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 informationSection 1 Simple Harmonic Motion. Chapter 11. Preview. Objectives Hooke s Law Sample Problem Simple Harmonic Motion The Simple Pendulum
Section 1 Simple Harmonic Motion Preview Objectives Hooke s Law Sample Problem Simple Harmonic Motion The Simple Pendulum Section 1 Simple Harmonic Motion Objectives Identify the conditions of simple harmonic
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 16: Oscillatory Motion and Waves. Simple Harmonic Motion (SHM)
Chapter 6: Oscillatory Motion and Waves Hooke s Law (revisited) F = - k x Tthe elastic potential energy of a stretched or compressed spring is PE elastic = kx / Spring-block Note: To consider the potential
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 informationSection 1 Simple Harmonic Motion. The student is expected to:
Section 1 Simple Harmonic Motion TEKS The student is expected to: 7A examine and describe oscillatory motion and wave propagation in various types of media Section 1 Simple Harmonic Motion Preview Objectives
More informationSIMPLE HARMONIC MOTION
WAVES SIMPLE HARMONIC MOTION Simple Harmonic Motion (SHM) Vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium TYPES OF SHM THE PENDULUM
More informationspring mass equilibrium position +v max
Lecture 20 Oscillations (Chapter 11) Review of Simple Harmonic Motion Parameters Graphical Representation of SHM Review of mass-spring pendulum periods Let s review Simple Harmonic Motion. Recall we used
More information(Total 1 mark) IB Questionbank Physics 1
1. A transverse wave travels from left to right. The diagram below shows how, at a particular instant of time, the displacement of particles in the medium varies with position. Which arrow represents the
More informationChapter 11 Vibrations and Waves
Chapter 11 Vibrations and Waves 11-1 Simple Harmonic Motion 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.
More information(Total 1 mark) IB Questionbank Physics 1
1. A transverse wave travels from left to right. The diagram below shows how, at a particular instant of time, the displacement of particles in the medium varies with position. Which arrow represents the
More information2016 AP Physics Unit 6 Oscillations and Waves.notebook December 09, 2016
AP Physics Unit Six Oscillations and Waves 1 2 A. Dynamics of SHM 1. Force a. since the block is accelerating, there must be a force acting on it b. Hooke's Law F = kx F = force k = spring constant x =
More informationOscillations - AP Physics B 1984
Oscillations - AP Physics B 1984 1. If the mass of a simple pendulum is doubled but its length remains constant, its period is multiplied by a factor of (A) 1 2 (B) (C) 1 1 2 (D) 2 (E) 2 A block oscillates
More informationCHAPTER 4 TEST REVIEW
IB PHYSICS Name: Period: Date: # Marks: 74 Raw Score: IB Curve: DEVIL PHYSICS BADDEST CLASS ON CAMPUS CHAPTER 4 TEST REVIEW 1. In which of the following regions of the electromagnetic spectrum is radiation
More informationMechanical Energy and Simple Harmonic Oscillator
Mechanical Energy and Simple Harmonic Oscillator Simple Harmonic Motion Hooke s Law Define system, choose coordinate system. Draw free-body diagram. Hooke s Law! F spring =!kx ˆi! kx = d x m dt Checkpoint
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 15. Mechanical Waves
Chapter 15 Mechanical Waves A wave is any disturbance from an equilibrium condition, which travels or propagates with time from one region of space to another. A harmonic wave is a periodic wave in which
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 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 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 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 informationUnit 2: Simple Harmonic Motion (SHM)
Unit 2: Simple Harmonic Motion (SHM) THE MOST COMMON FORM OF MOTION FALL 2015 Objectives: Define SHM specifically and give an example. Write and apply formulas for finding the frequency f, period T, w
More informationPhysics 1C. Lecture 12B
Physics 1C Lecture 12B SHM: Mathematical Model! Equations of motion for SHM:! Remember, simple harmonic motion is not uniformly accelerated motion SHM: Mathematical Model! The maximum values of velocity
More informationFaculty of Computers and Information Fayoum University 2017/ 2018 Physics 2 (Waves)
Faculty of Computers and Information Fayoum University 2017/ 2018 Physics 2 (Waves) 3/10/2018 1 Using these definitions, we see that Example : A sinusoidal wave traveling in the positive x direction has
More informationf 1/ T T 1/ f Formulas Fs kx m T s 2 k l T p 2 g v f
f 1/T Formulas T 1/ f Fs kx Ts 2 m k Tp 2 l g v f What do the following all have in common? Swing, pendulum, vibrating string They all exhibit forms of periodic motion. Periodic Motion: When a vibration
More informationLecture 17. Mechanical waves. Transverse waves. Sound waves. Standing Waves.
Lecture 17 Mechanical waves. Transverse waves. Sound waves. Standing Waves. What is a wave? A wave is a traveling disturbance that transports energy but not matter. Examples: Sound waves (air moves back
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 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 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 informationChapter 16 Waves in One Dimension
Lecture Outline Chapter 16 Waves in One Dimension Slide 16-1 Chapter 16: Waves in One Dimension Chapter Goal: To study the kinematic and dynamics of wave motion, i.e., the transport of energy through a
More information1 f. result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by
result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by amplitude (how far do the bits move from their equilibrium positions? Amplitude of MEDIUM)
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 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 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 information1. Types of Waves. There are three main types of waves:
Chapter 16 WAVES I 1. Types of Waves There are three main types of waves: https://youtu.be/kvc7obkzq9u?t=3m49s 1. Mechanical waves: These are the most familiar waves. Examples include water waves, sound
More informationNARAYANA JUNIOR COLLEGE
SR IIT ALL STREAMS ADV MODEL DPT-6 Date: 18/04/2016 One (or) More Than One Answer Type: PHYSICS 31. A particle is executing SHM between points -X m and X m, as shown in figure-i. The velocity V(t) of the
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 informationGeneral Physics I Spring Oscillations
General Physics I Spring 2011 Oscillations 1 Oscillations A quantity is said to exhibit oscillations if it varies with time about an equilibrium or reference value in a repetitive fashion. Oscillations
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 informationSimple Harmonic Motion
3/5/07 Simple Harmonic Motion 0. The Ideal Spring and Simple Harmonic Motion HOOKE S AW: RESTORING FORCE OF AN IDEA SPRING The restoring force on an ideal spring is F x k x spring constant Units: N/m 3/5/07
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 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 informationChapter 13. Simple Harmonic Motion
Chapter 13 Simple Harmonic Motion Hooke s Law F s = - k x F s is the spring force k is the spring constant It is a measure of the stiffness of the spring A large k indicates a stiff spring and a small
More informationChapter 11. Vibrations and Waves
Chapter 11 Vibrations and Waves Driven Harmonic Motion and Resonance RESONANCE Resonance is the condition in which a time-dependent force can transmit large amounts of energy to an oscillating object,
More informationUnforced Mechanical Vibrations
Unforced Mechanical Vibrations Today we begin to consider applications of second order ordinary differential equations. 1. Spring-Mass Systems 2. Unforced Systems: Damped Motion 1 Spring-Mass Systems We
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 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 informationA body is displaced from equilibrium. State the two conditions necessary for the body to execute simple harmonic motion
1. Simple harmonic motion and the greenhouse effect (a) A body is displaced from equilibrium. State the two conditions necessary for the body to execute simple harmonic motion. 1. 2. (b) In a simple model
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 informationChapter 11 Vibrations and Waves
Chapter 11 Vibrations and Waves 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
More informationEXAM 1. WAVES, OPTICS AND MODERN PHYSICS 15% of the final mark
EXAM 1 WAVES, OPTICS AND MODERN PHYSICS 15% of the final mark Autumn 2018 Name: Each multiple-choice question is worth 3 marks. 1. A light beam is deflected by two mirrors, as shown. The incident beam
More informationOscillations and Waves
Oscillations and Waves Periodic Motion Simple Harmonic Motion Connections between Uniform Circular Motion and Simple Harmonic Motion The Period of a Mass on a Spring Energy Conservation in Oscillatory
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 15 Mechanical Waves
Chapter 15 Mechanical Waves 1 Types of Mechanical Waves This chapter and the next are about mechanical waves waves that travel within some material called a medium. Waves play an important role in how
More informationSimple Harmonic Motion. Harmonic motion due to a net restoring force directly proportional to the displacement
Simple Harmonic Motion Harmonic motion due to a net restoring force directly proportional to the displacement Eample: Spring motion: F = -k Net Force: d! k = m dt " F = ma d dt + k m = 0 Equation of motion
More informationExam 3 Review. Chapter 10: Elasticity and Oscillations A stress will deform a body and that body can be set into periodic oscillations.
Exam 3 Review Chapter 10: Elasticity and Oscillations stress will deform a body and that body can be set into periodic oscillations. Elastic Deformations of Solids Elastic objects return to their original
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 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 informationSchedule for the remainder of class
Schedule for the remainder of class 04/25 (today): Regular class - Sound and the Doppler Effect 04/27: Cover any remaining new material, then Problem Solving/Review (ALL chapters) 04/29: Problem Solving/Review
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 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 informationChapter 13, Vibrations and Waves. 1. A large spring requires a force of 150 N to compress it only m. What is the spring constant of the spring?
CHAPTER 13 1. A large spring requires a force of 150 N to compress it only 0.010 m. What is the spring constant of the spring? a. 125 000 N/m b. 15 000 N/m c. 15 N/m d. 1.5 N/m 2. A 0.20-kg object is attached
More informationChapter 16 Mechanical Waves
Chapter 6 Mechanical Waves A wave is a disturbance that travels, or propagates, without the transport of matter. Examples: sound/ultrasonic wave, EM waves, and earthquake wave. Mechanical waves, such as
More informationWhat is a Wave. Why are Waves Important? Power PHYSICS 220. Lecture 19. Waves
PHYSICS 220 Lecture 19 Waves What is a Wave A wave is a disturbance that travels away from its source and carries energy. A wave can transmit energy from one point to another without transporting any matter
More informationChapter 12 Vibrations and Waves Simple Harmonic Motion page
Chapter 2 Vibrations and Waves 2- Simple Harmonic Motion page 438-45 Hooke s Law Periodic motion the object has a repeated motion that follows the same path, the object swings to and fro. Examples: a pendulum
More informationAP Physics C Mechanics
1 AP Physics C Mechanics Simple Harmonic Motion 2015 12 05 www.njctl.org 2 Table of Contents Click on the topic to go to that section Spring and a Block Energy of SHM SHM and UCM Simple and Physical Pendulums
More informationα(t) = ω 2 θ (t) κ I ω = g L L g T = 2π mgh rot com I rot
α(t) = ω 2 θ (t) ω = κ I ω = g L T = 2π L g ω = mgh rot com I rot T = 2π I rot mgh rot com Chapter 16: Waves Mechanical Waves Waves and particles Vibration = waves - Sound - medium vibrates - Surface ocean
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 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 14 Preview Looking Ahead
Chapter 14 Preview Looking Ahead Text: p. 438 Slide 14-1 Chapter 14 Preview Looking Back: Springs and Restoring Forces In Chapter 8, you learned that a stretched spring exerts a restoring force proportional
More informationCh 3.7: Mechanical & Electrical Vibrations
Ch 3.7: Mechanical & Electrical Vibrations Two important areas of application for second order linear equations with constant coefficients are in modeling mechanical and electrical oscillations. We will
More informationApr 29, 2013 PHYSICS I Lecture 22
95.141 Apr 29, 2013 PHYSICS I Lecture 22 Course website: faculty.uml.edu/pchowdhury/95.141/ www.masteringphysics.com Course: UML95141SPRING2013 Lecture Capture h"p://echo360.uml.edu/chowdhury2013/physics1spring.html
More informationChapter The spring stretched (85cm - 65cm) when the force was increased.. 180N. =. Solve for k.
Chapter 11 1. The amplitude is ½ the total vertical distance, and a simple harmonic oscillator travels twice the vertical distance in one oscillation. 2. The spring stretched (85cm - 65cm) when the force
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 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 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 informationSIMPLE PENDULUM AND PROPERTIES OF SIMPLE HARMONIC MOTION
SIMPE PENDUUM AND PROPERTIES OF SIMPE HARMONIC MOTION Purpose a. To investigate the dependence of time period of a simple pendulum on the length of the pendulum and the acceleration of gravity. b. To study
More informationa) period will increase b) period will not change c) period will decrease
Physics 101 Tuesday 11/3/11 Class 21" Chapter 13.4 13.7" Period of a mass on a spring" Energy conservation in oscillations" Pendulum" Damped oscillations" " A glider with a spring attached to each end
More informationWhat is a wave? Waves
What is a wave? Waves Waves What is a wave? A wave is a disturbance that carries energy from one place to another. Classifying waves 1. Mechanical Waves - e.g., water waves, sound waves, and waves on strings.
More informationCHAPTER 11 TEST REVIEW
AP PHYSICS Name: Period: Date: 50 Multiple Choice 45 Single Response 5 Multi-Response Free Response 3 Short Free Response 2 Long Free Response DEVIL PHYSICS BADDEST CLASS ON CAMPUS AP EXAM CHAPTER TEST
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 informationStanding waves [49 marks]
Standing waves [49 marks] 1. The graph shows the variation with time t of the velocity v of an object undergoing simple harmonic motion (SHM). At which velocity does the displacement from the mean position
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 11-1: SIMPLE HARMONIC MOTION LSN 11-: ENERGY IN THE SIMPLE HARMONIC OSCILLATOR LSN 11-3: PERIOD AND THE SINUSOIDAL NATURE OF SHM Introductory Video:
More information1 A mass on a spring undergoes SHM. The maximum displacement from the equilibrium is called?
Slide 1 / 20 1 mass on a spring undergoes SHM. The maximum displacement from the equilibrium is called? Period Frequency mplitude Wavelength Speed Slide 2 / 20 2 In a periodic process, the number of cycles
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 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 informationAP Physics 1. April 11, Simple Harmonic Motion. Table of Contents. Period. SHM and Circular Motion
AP Physics 1 2016-07-20 www.njctl.org Table of Contents Click on the topic to go to that section Period and Frequency SHM and UCM Spring Pendulum Simple Pendulum Sinusoidal Nature of SHM Period and Frequency
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 informationEXERCISE - 01 NEETIIT.COM. d x dt. = 2 x 2 (4)
1. The acceleration of a particle executing S.H.M. is (1) Always directed towards the equillibrium position () Always towards the one end (3) Continuously changing in direction () Maximum at the mean position.
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 informationChapter 16 Lectures. Oscillatory Motion and Waves
Chapter 16 Lectures January-06-18 5:48 PM Oscillatory Motion and Waves Oscillations are back-and-forth motions. Sometimes the word vibration is used in place of oscillation; for our purposes, we can consider
More information8.91 Problems. for Section 8.1, 8-1: Why does KE increase more in the first quartercycle
8.91 Problems for Section 8.1, 8-1: Why does KE increase more in the first quartercycle (it goes from 0 J to 3 J) than in the second quartercycle (3 J to 4 J). 8-2: How many ways can you think of to change
More information