Simple Harmonic Motion of Spring

Size: px
Start display at page:

Download "Simple Harmonic Motion of Spring"

Transcription

1 Nae P Physics Date iple Haronic Motion and prings Hooean pring W x U ( x iple Haronic Motion of pring. What are the two criteria for siple haronic otion? - Only restoring forces cause siple haronic otion. restoring force is a force that it proportional to the displaceent fro equilibriu and in the opposite direction. - Position, velocity and the other variables of siple haronic otion are sinusoidal functions of tie.. he diagra to the right shows a g bloc attached to a Hooean spring on a frictionless surface. he bloc experiences no net force when it is at position. When the bloc is to the left of point the spring pushes it to the right. When the bloc is to the right of point, the spring pulls it to the left. he ass is pulled to the right fro point to point and released at tie t =. he bloc then oscillates between positions and. ssue that the syste consists of the bloc and the spring and that no dissipative forces act. a) he bloc taes 4. s to ae oscillations. What is the period of oscillation for this syste? = 4s/ oscillations = sec/oscillation b) What is the frequency of this oscillating syste? f = / = ½ =.5 Hz c) What is the aplitude of vibration of this syste? =. d) Deterine the spring constant of the spring. ) x cos( t) cos( a e) Write an equation that describes the position of the ass as a function of tie, starting fro position at tie t =. x. cos(. cos( t) x 9.7N /

2 f) Explain what would happen to the period and frequency of this syste if you were to double the aplitude while eeping the ass and spring constant the sae. he period and frequency would not change since they do not depend on the aplitude of oscillation g) Explain what would happen to the period and frequency of this syste if you were to double the ass while eeping the aplitude and spring constant the sae. period depends on square root of ass so if ass doubled, would change by frequency depends on /( ) so if ass doubled, f would change by / =.7 x x.4 f.7f h) Explain what would happen to the period and frequency of this syste if you were to double the spring constant while eeping the aplitude and ass constant. period depends on /( ) so if spring constant doubled, would change by / =.7x frequency depends on square root of so if spring constant doubled, f would change by x f.4f x x i) Deterine the aount of energy of the oscillating spring and ass syste. he energy of the bloc and spring is conserved since only the spring force (a conservative force) does wor. herefore E = E = E E = E = ½ (x ) = ½ (9.7)( ) =.394J.7, j) Where does the bloc have axiu speed and what is the axiu speed? loc has axiu speed at point, the equilibriu point of the spring. t that point, all the energy is in the for of inetic energy E E V.394 v () v.63 ) Where does the bloc experience axiu acceleration and what is the axiu acceleration? loc has axiu acceleration at points and, at ax displaceent fro equilibriu, where net = s pring is greatest a x (9.7)(.).97 l) What would happen to the energy if the aplitude of oscillation were tripled while eeping the ass and spring constant unchanged? he energy is proportional to the aplitude squared (E = ½ ). herefore, if the aplitude of the oscillation were tripled, the total energy would increase 9xs. ) What would happen to the axiu speed if the aplitude of oscillation were tripled while eeping the ass and spring constant unchanged? he ax speed at equilib is proportional to the aplitude (E =E = ½ = ½ v ). herefore, if the aplitude of the oscillation were tripled, the ax speed would also triple.

3 3. 5 g ass is attached to a spring that is hanging vertically. he spring is stretched.5 fro its equilibriu position. a) What is the spring constant? x g g g x 96N / x=.5 b) What ass would be required to stretch the spring three ties the distance? g 3xs or 5 g since the ass is directly proportional to the displaceent he 5 g object hanging on the spring is allowed to coe to its new equilibriu. It is then set in otion by stretching it a further.3. he ass oscillates in siple haronic otion c) What is the period of the oscillation? 5. s g ass on a spring is stretched and released. he period of oscillation is easured to be.46 s. What is the spring constant? N / 5. weight in a spring-ass syste exhibits haronic otion. he syste is in equilibriu when the weight is otionless. If the weight is pulled down or pushed up and released, it would tend to oscillate freely if there were no friction. In a certain spring-ass syste, the weight is 5 feet below a -foot ceiling when it is at rest. he otion of the weight can be described by the equation, y = 3sin(t), where y is the distance fro the equilibriu point, and t is easured in seconds. a) ind the period of the otion. seconds. he expression in the sin function, t, is equal to ft. herefore f =.5s and = s b) What is the frequency of the otion? / cycle per second. c) ind the aplitude of the otion. 3ft d) How far fro the ceiling is the weight after 3.5 seconds? 8 ft sp

4 6. he graph in the figure shows the displaceent of a.4 g particle fro a fixed equilibriu position. Z Z V V Z Use the graph to deterine: a) the period of otion Period is tie of cycle =.s b) the axiu speed of the particle during oscillation, he ax speed is when the object passes through the equilibriu where there is no elastic potential energy. Rather all the energy is in the for of inetic energy. he energy of the particle and spring is conserved since only the spring force (a conservative force) does wor. We need to find the echanical energy before finding the ax speed. E = E = ½ = ½ (4)( ) = 8J E = E = ½v = ½(.4)v = 8J v = 63. /s.4. 4N / c) the axiu acceleration experienced by the particle. Particle has axiu acceleration at ax displaceent fro equilibriu, where net = s pring is greatest x (4)() a.4 ax ax / On the graph, ar the following a) a point where the velocity is zero ( label this as Z) b) a point where the velocity is positive and has the largest agnitude ( label this as V) c) a point where the acceleration is positive and has the largest agnitude ( label this as ). s

5 Kinetic E Potential E net (N) slope a (/s ) v (/s) slope x () Motion sensor 4.c 7. he diagra above shows a g bloc attached to a Hooean spring on a frictionless surface. he bloc experiences no net force when it is at position. When the bloc is to the left of point the spring pushes it to the right. When the bloc is to the right of point, the spring pulls it to the left. he ass is pulled to the left fro point to point and released. he bloc then oscillates between positions and. otion sensor placed to the right of position gathers position-tie data for the oscillating bloc. he position vs. tie graph below describes the otion of this syste for four cycles sec x(t)=.3sin(+.5 =.3sin(t)+.5 v(t)=.9cos( =.9cos(t) a(t)= -.8sin( = -.8sin(t) (t)= -3.6sin( = -3.6sin(t) J 3.5J U (t)= ½(x ) = 3.5sin (t) K(t)= ½v = 3.5cos (t)

6 a) What is the period of oscillation for this syste? = sec b) What is the frequency of this oscillating syste? f = / = Hz c) U (t)= ½(x ) = 3.5sin (t) d) What is the aplitude of vibration of this syste? =.3 e) Deterine the spring constant of the spring f) oplete setches for the other graphs shown based on the position vs. tie graph. Label axia and inia with nuerical values on the axes. oe things to consider when you setch the graphs: - You can ae qualitative v-t and a-t setches by considering the slopes of appropriate graphs o get a qualitative v-t graph (no nubers), tae the slope of the x-t graph at points where it is zero, ax or in and plot the v-t points shown. onnect points with a sinusoidal curve o get a qualitative a-t graph (no nubers), tae the slope of the v-t graph at points where it is zero, ax or in and plot the a-t points shown. onnect points with a sinusoidal curve -t graph loos qualitatively lie a-t since they are directly related by ultiplying by the scalar. Energy graphs are related to x (potential) and v (inetic) so the negative regions on the x-t or v-t becoe positive on the energy graphs. - Reeber that Us = ½ x where x = x-x is displaceent fro equilibriu (x = at the equilibriu position) Us is NO ½ x when x = at the otion sensor. - Reeber that a = net/ = (-x)/ how calculations necessary to label the graphs (ax and in values of each variable) Velocity Graph cceleration Graph v ax is at the equilibriu point where all the energy is inetic energy. he energy of the ass-spring syste is conserved at every position; E = E = E = E x v( t) vax cos( v E v v v E orce Graph ax 78.7(.3.88 net net a a ) ax (.8) 3.6N cos( 78.7N / a( t) aax sin( Max acceleration is at ax displaceent (x=). net x a a ax ax (78.7)(.3) a a a.8 ax

7 Potential Energy Graph U is proportional to x, not to x. x = x-x where x is the equilibriu position of the spring and bloc. ro the x(t) graph, you can see that x is.5. Zero potential energy can be set anywhere. or convenience, define it to be the equilibriu point of the spring and bloc. Max U is at ax x which is the aplitude (.3) ( ) 3.54J KineticEnergy Graph has sae ax as Potential E graph since energy is conserved g) What is the average velocity of the bloc during one cycle? v x U U ax ( x ) h) What is the average speed of the bloc during one cycle? In one cycle, the distance travelled can be seen on the x-t graph s d.. s / i) If the frequency of the oscillation were doubled, what would the average speed of the bloc be during one cycle? he average speed would double since the bloc would travel the sae distance in ½ the tie d. s.4.5

m A 1 m mgd k m v ( C) AP Physics Multiple Choice Practice Oscillations

m A 1 m mgd k m v ( C) AP Physics Multiple Choice Practice Oscillations P Physics Multiple Choice Practice Oscillations. ass, attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is.

More information

WileyPLUS Assignment 3. Next Week

WileyPLUS Assignment 3. Next Week WileyPLUS Assignent 3 Chapters 6 & 7 Due Wednesday, Noveber 11 at 11 p Next Wee No labs of tutorials Reebrance Day holiday on Wednesday (no classes) 24 Displaceent, x Mass on a spring ωt = 2π x = A cos

More information

CHECKLIST. r r. Newton s Second Law. natural frequency ω o (rad.s -1 ) (Eq ) a03/p1/waves/waves doc 9:19 AM 29/03/05 1

CHECKLIST. r r. Newton s Second Law. natural frequency ω o (rad.s -1 ) (Eq ) a03/p1/waves/waves doc 9:19 AM 29/03/05 1 PHYS12 Physics 1 FUNDAMENTALS Module 3 OSCILLATIONS & WAVES Text Physics by Hecht Chapter 1 OSCILLATIONS Sections: 1.5 1.6 Exaples: 1.6 1.7 1.8 1.9 CHECKLIST Haronic otion, periodic otion, siple haronic

More information

Page 1. Physics 131: Lecture 22. Today s Agenda. SHM and Circles. Position

Page 1. Physics 131: Lecture 22. Today s Agenda. SHM and Circles. Position Physics 3: ecture Today s genda Siple haronic otion Deinition Period and requency Position, velocity, and acceleration Period o a ass on a spring Vertical spring Energy and siple haronic otion Energy o

More information

L 2. AP Physics Free Response Practice Oscillations ANSWERS 1975B7. (a) F T2. (b) F NET(Y) = 0

L 2. AP Physics Free Response Practice Oscillations ANSWERS 1975B7. (a) F T2. (b) F NET(Y) = 0 AP Physics Free Response Practice Oscillations ANSWERS 1975B7. (a) 60 F 1 F g (b) F NE(Y) = 0 F1 F1 = g / cos(60) = g (c) When the string is cut it swings fro top to botto, siilar to the diagra for 1974B1

More information

Periodic Motion is everywhere

Periodic Motion is everywhere Lecture 19 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand and use energy conservation

More information

Student Book pages

Student Book pages Chapter 7 Review Student Boo pages 390 39 Knowledge. Oscillatory otion is otion that repeats itself at regular intervals. For exaple, a ass oscillating on a spring and a pendulu swinging bac and forth..

More information

Problem Set 14: Oscillations AP Physics C Supplementary Problems

Problem Set 14: Oscillations AP Physics C Supplementary Problems Proble Set 14: Oscillations AP Physics C Suppleentary Probles 1 An oscillator consists of a bloc of ass 050 g connected to a spring When set into oscillation with aplitude 35 c, it is observed to repeat

More information

More Oscillations! (Today: Harmonic Oscillators)

More Oscillations! (Today: Harmonic Oscillators) More Oscillations! (oday: Haronic Oscillators) Movie assignent reinder! Final due HURSDAY April 20 Subit through ecapus Different rubric; reeber to chec it even if you got 00% on your draft: http://sarahspolaor.faculty.wvu.edu/hoe/physics-0

More information

TUTORIAL 1 SIMPLE HARMONIC MOTION. Instructor: Kazumi Tolich

TUTORIAL 1 SIMPLE HARMONIC MOTION. Instructor: Kazumi Tolich TUTORIAL 1 SIMPLE HARMONIC MOTION Instructor: Kazui Tolich About tutorials 2 Tutorials are conceptual exercises that should be worked on in groups. Each slide will consist of a series of questions that

More information

Q5 We know that a mass at the end of a spring when displaced will perform simple m harmonic oscillations with a period given by T = 2!

Q5 We know that a mass at the end of a spring when displaced will perform simple m harmonic oscillations with a period given by T = 2! Chapter 4.1 Q1 n oscillation is any otion in which the displaceent of a particle fro a fixed point keeps changing direction and there is a periodicity in the otion i.e. the otion repeats in soe way. In

More information

Physics 207 Lecture 18. Physics 207, Lecture 18, Nov. 3 Goals: Chapter 14

Physics 207 Lecture 18. Physics 207, Lecture 18, Nov. 3 Goals: Chapter 14 Physics 07, Lecture 18, Nov. 3 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand

More information

2. Which of the following best describes the relationship between force and potential energy?

2. Which of the following best describes the relationship between force and potential energy? Work/Energy with Calculus 1. An object oves according to the function x = t 5/ where x is the distance traveled and t is the tie. Its kinetic energy is proportional to (A) t (B) t 5/ (C) t 3 (D) t 3/ (E)

More information

Simple Harmonic Motion

Simple Harmonic Motion Reading: Chapter 15 Siple Haronic Motion Siple Haronic Motion Frequency f Period T T 1. f Siple haronic otion x ( t) x cos( t ). Aplitude x Phase Angular frequency Since the otion returns to its initial

More information

Waves Unit I Activity: Kinematic Equations for SHM

Waves Unit I Activity: Kinematic Equations for SHM Nae Date Period Waves Unit I Activity: Kineatic Equations for SHM You have seen four different graphs in the wor you have done on ass-spring systes oscillating in siple haronic otion (SHM). Now we will

More information

Physics 4A Solutions to Chapter 15 Homework

Physics 4A Solutions to Chapter 15 Homework Physics 4A Solutions to Chapter 15 Hoework Chapter 15 Questions:, 8, 1 Exercises & Probles 6, 5, 31, 41, 59, 7, 73, 88, 90 Answers to Questions: Q 15- (a) toward -x (b) toward +x (c) between -x and 0 (d)

More information

PHYS 1443 Section 003 Lecture #22

PHYS 1443 Section 003 Lecture #22 PHYS 443 Section 003 Lecture # Monda, Nov. 4, 003. Siple Bloc-Spring Sste. Energ of the Siple Haronic Oscillator 3. Pendulu Siple Pendulu Phsical Pendulu orsion Pendulu 4. Siple Haronic Motion and Unifor

More information

Page 1. Physics 131: Lecture 22. SHM and Circles. Today s Agenda. Position. Velocity. Position and Velocity. Acceleration. v Asin.

Page 1. Physics 131: Lecture 22. SHM and Circles. Today s Agenda. Position. Velocity. Position and Velocity. Acceleration. v Asin. Physics 3: ecture Today s enda Siple haronic otion Deinition Period and requency Position, velocity, and acceleration Period o a ass on a sprin Vertical sprin Enery and siple haronic otion Enery o a sprin

More information

27 Oscillations: Introduction, Mass on a Spring

27 Oscillations: Introduction, Mass on a Spring Chapter 7 Oscillations: Introduction, Mass on a Spring 7 Oscillations: Introduction, Mass on a Spring If a siple haronic oscillation proble does not involve the tie, you should probably be using conservation

More information

CHAPTER 15: Vibratory Motion

CHAPTER 15: Vibratory Motion CHAPTER 15: Vibratory Motion courtesy of Richard White courtesy of Richard White 2.) 1.) Two glaring observations can be ade fro the graphic on the previous slide: 1.) The PROJECTION of a point on a circle

More information

Question 1. [14 Marks]

Question 1. [14 Marks] 6 Question 1. [14 Marks] R r T! A string is attached to the dru (radius r) of a spool (radius R) as shown in side and end views here. (A spool is device for storing string, thread etc.) A tension T is

More information

Oscillations: Review (Chapter 12)

Oscillations: Review (Chapter 12) Oscillations: Review (Chapter 1) Oscillations: otions that are periodic in tie (i.e. repetitive) o Swinging object (pendulu) o Vibrating object (spring, guitar string, etc.) o Part of ediu (i.e. string,

More information

9 HOOKE S LAW AND SIMPLE HARMONIC MOTION

9 HOOKE S LAW AND SIMPLE HARMONIC MOTION Experient 9 HOOKE S LAW AND SIMPLE HARMONIC MOTION Objectives 1. Verify Hoo s law,. Measure the force constant of a spring, and 3. Measure the period of oscillation of a spring-ass syste and copare it

More information

Simple and Compound Harmonic Motion

Simple and Compound Harmonic Motion Siple Copound Haronic Motion Prelab: visit this site: http://en.wiipedia.org/wii/noral_odes Purpose To deterine the noral ode frequencies of two systes:. a single ass - two springs syste (Figure );. two

More information

= T. Oscillations and Waves. Example of an Oscillating System IB 12 IB 12

= T. Oscillations and Waves. Example of an Oscillating System IB 12 IB 12 Oscillation: the vibration of an object Oscillations and Waves Eaple of an Oscillating Syste A ass oscillates on a horizontal spring without friction as shown below. At each position, analyze its displaceent,

More information

Simple Harmonic Motion

Simple Harmonic Motion Siple Haronic Motion Physics Enhanceent Prograe for Gifted Students The Hong Kong Acadey for Gifted Education and Departent of Physics, HKBU Departent of Physics Siple haronic otion In echanical physics,

More information

Physics 2107 Oscillations using Springs Experiment 2

Physics 2107 Oscillations using Springs Experiment 2 PY07 Oscillations using Springs Experient Physics 07 Oscillations using Springs Experient Prelab Read the following bacground/setup and ensure you are failiar with the concepts and theory required for

More information

Lecture #8-3 Oscillations, Simple Harmonic Motion

Lecture #8-3 Oscillations, Simple Harmonic Motion Lecture #8-3 Oscillations Siple Haronic Motion So far we have considered two basic types of otion: translation and rotation. But these are not the only two types of otion we can observe in every day life.

More information

Flipping Physics Lecture Notes: Free Response Question #1 - AP Physics Exam Solutions

Flipping Physics Lecture Notes: Free Response Question #1 - AP Physics Exam Solutions 2015 FRQ #1 Free Response Question #1 - AP Physics 1-2015 Exa Solutions (a) First off, we know both blocks have a force of gravity acting downward on the. et s label the F & F. We also know there is a

More information

PHYS 1443 Section 003 Lecture #21 Wednesday, Nov. 19, 2003 Dr. Mystery Lecturer

PHYS 1443 Section 003 Lecture #21 Wednesday, Nov. 19, 2003 Dr. Mystery Lecturer PHYS 443 Section 003 Lecture # Wednesday, Nov. 9, 003 Dr. Mystery Lecturer. Fluid Dyanics : Flow rate and Continuity Equation. Bernoulli s Equation 3. Siple Haronic Motion 4. Siple Bloc-Spring Syste 5.

More information

PY241 Solutions Set 9 (Dated: November 7, 2002)

PY241 Solutions Set 9 (Dated: November 7, 2002) PY241 Solutions Set 9 (Dated: Noveber 7, 2002) 9-9 At what displaceent of an object undergoing siple haronic otion is the agnitude greatest for the... (a) velocity? The velocity is greatest at x = 0, the

More information

Discussion Examples Chapter 13: Oscillations About Equilibrium

Discussion Examples Chapter 13: Oscillations About Equilibrium Discussion Exaples Chapter 13: Oscillations About Equilibriu 17. he position of a ass on a spring is given by x 6.5 c cos t 0.88 s. (a) What is the period,, of this otion? (b) Where is the ass at t 0.5

More information

Physics 140 D100 Midterm Exam 2 Solutions 2017 Nov 10

Physics 140 D100 Midterm Exam 2 Solutions 2017 Nov 10 There are 10 ultiple choice questions. Select the correct answer for each one and ark it on the bubble for on the cover sheet. Each question has only one correct answer. (2 arks each) 1. An inertial reference

More information

VIBRATING SYSTEMS. example. Springs obey Hooke s Law. Terminology. L 21 Vibration and Waves [ 2 ]

VIBRATING SYSTEMS. example. Springs obey Hooke s Law. Terminology. L 21 Vibration and Waves [ 2 ] L 1 Vibration and Waves [ ] Vibrations (oscillations) resonance pendulu springs haronic otion Waves echanical waves sound waves usical instruents VIBRATING SYSTEMS Mass and spring on air trac Mass hanging

More information

T m. Fapplied. Thur Oct 29. ω = 2πf f = (ω/2π) T = 1/f. k m. ω =

T m. Fapplied. Thur Oct 29. ω = 2πf f = (ω/2π) T = 1/f. k m. ω = Thur Oct 9 Assignent 10 Mass-Spring Kineatics (x, v, a, t) Dynaics (F,, a) Tie dependence Energy Pendulu Daping and Resonances x Acos( ωt) = v = Aω sin( ωt) a = Aω cos( ωt) ω = spring k f spring = 1 k

More information

For a situation involving gravity near earth s surface, a = g = jg. Show. that for that case v 2 = v 0 2 g(y y 0 ).

For a situation involving gravity near earth s surface, a = g = jg. Show. that for that case v 2 = v 0 2 g(y y 0 ). Reading: Energy 1, 2. Key concepts: Scalar products, work, kinetic energy, work-energy theore; potential energy, total energy, conservation of echanical energy, equilibriu and turning points. 1.! In 1-D

More information

Force and dynamics with a spring, analytic approach

Force and dynamics with a spring, analytic approach Force and dynaics with a spring, analytic approach It ay strie you as strange that the first force we will discuss will be that of a spring. It is not one of the four Universal forces and we don t use

More information

Pearson Physics Level 20 Unit IV Oscillatory Motion and Mechanical Waves: Unit IV Review Solutions

Pearson Physics Level 20 Unit IV Oscillatory Motion and Mechanical Waves: Unit IV Review Solutions Pearson Physics Level 0 Unit IV Oscillatory Motion and Mechanical Waves: Unit IV Review Solutions Student Book pages 440 443 Vocabulary. aplitude: axiu displaceent of an oscillation antinodes: points of

More information

OSCILLATIONS AND WAVES

OSCILLATIONS AND WAVES OSCILLATIONS AND WAVES OSCILLATION IS AN EXAMPLE OF PERIODIC MOTION No stories this tie, we are going to get straight to the topic. We say that an event is Periodic in nature when it repeats itself in

More information

A body of unknown mass is attached to an ideal spring with force constant 123 N/m. It is found to vibrate with a frequency of

A body of unknown mass is attached to an ideal spring with force constant 123 N/m. It is found to vibrate with a frequency of Chapter 14 [ Edit ] Overview Suary View Diagnostics View Print View with Answers Chapter 14 Due: 11:59p on Sunday, Noveber 27, 2016 To understand how points are awarded, read the Grading Policy for this

More information

Course Information. Physics 1C Waves, optics and modern physics. Grades. Class Schedule. Clickers. Homework

Course Information. Physics 1C Waves, optics and modern physics. Grades. Class Schedule. Clickers. Homework Course Inforation Physics 1C Waves, optics and odern physics Instructor: Melvin Oaura eail: oaura@physics.ucsd.edu Course Syllabus on the web page http://physics.ucsd.edu/ students/courses/fall2009/physics1c

More information

5/09/06 PHYSICS 213 Exam #1 NAME FEYNMAN Please write down your name also on the back side of the last page

5/09/06 PHYSICS 213 Exam #1 NAME FEYNMAN Please write down your name also on the back side of the last page 5/09/06 PHYSICS 13 Exa #1 NAME FEYNMAN Please write down your nae also on the back side of the last page 1 he figure shows a horizontal planks of length =50 c, and ass M= 1 Kg, pivoted at one end. he planks

More information

Physics 41 HW Set 1 Chapter 15 Serway 7 th Edition

Physics 41 HW Set 1 Chapter 15 Serway 7 th Edition Physics HW Set Chapter 5 Serway 7 th Edition Conceptual Questions:, 3, 5,, 6, 9 Q53 You can take φ = π, or equally well, φ = π At t= 0, the particle is at its turning point on the negative side of equilibriu,

More information

SHM stuff the story continues

SHM stuff the story continues SHM stuff the story continues Siple haronic Motion && + ω solution A cos t ( ω + α ) Siple haronic Motion + viscous daping b & + ω & + Viscous daping force A e b t Viscous daped aplitude Viscous daped

More information

PH 221-2A Fall Waves - I. Lectures Chapter 16 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition)

PH 221-2A Fall Waves - I. Lectures Chapter 16 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) PH 1-A Fall 014 Waves - I Lectures 4-5 Chapter 16 (Halliday/Resnick/Walker, Fundaentals of Physics 9 th edition) 1 Chapter 16 Waves I In this chapter we will start the discussion on wave phenoena. We will

More information

Common Exam 2 Physics 111 Fall 2006 Name A

Common Exam 2 Physics 111 Fall 2006 Name A Coon Ea Physics Fall 006 Nae A Total Nuber of Points is 5 (Multiple Choice and Worout Probles). Multiple Choice Probles are Point per Question..) A toy car oving at constant speed copletes one lap around

More information

which proves the motion is simple harmonic. Now A = a 2 + b 2 = =

which proves the motion is simple harmonic. Now A = a 2 + b 2 = = Worked out Exaples. The potential energy function for the force between two atos in a diatoic olecules can be expressed as follows: a U(x) = b x / x6 where a and b are positive constants and x is the distance

More information

Chapter 1: Basics of Vibrations for Simple Mechanical Systems

Chapter 1: Basics of Vibrations for Simple Mechanical Systems Chapter 1: Basics of Vibrations for Siple Mechanical Systes Introduction: The fundaentals of Sound and Vibrations are part of the broader field of echanics, with strong connections to classical echanics,

More information

Chapter 4 FORCES AND NEWTON S LAWS OF MOTION PREVIEW QUICK REFERENCE. Important Terms

Chapter 4 FORCES AND NEWTON S LAWS OF MOTION PREVIEW QUICK REFERENCE. Important Terms Chapter 4 FORCES AND NEWTON S LAWS OF MOTION PREVIEW Dynaics is the study o the causes o otion, in particular, orces. A orce is a push or a pull. We arrange our knowledge o orces into three laws orulated

More information

Experiment 2: Hooke s Law

Experiment 2: Hooke s Law COMSATS Institute of Inforation Technology, Islaabad Capus PHYS-108 Experient 2: Hooke s Law Hooke s Law is a physical principle that states that a spring stretched (extended) or copressed by soe distance

More information

Chapter 11 Simple Harmonic Motion

Chapter 11 Simple Harmonic Motion Chapter 11 Siple Haronic Motion "We are to adit no ore causes of natural things than such as are both true and sufficient to explain their appearances." Isaac Newton 11.1 Introduction to Periodic Motion

More information

Pearson Physics Level 20 Unit IV Oscillatory Motion and Mechanical Waves: Chapter 7 Solutions

Pearson Physics Level 20 Unit IV Oscillatory Motion and Mechanical Waves: Chapter 7 Solutions Pearson Physics Level 0 Unit IV Oscillatory Motion and Mechanical Waves: Chapter 7 Solutions Student Boo page 345 Exaple 7. Practice Probles. 60 s T 5.00 in in 300 s f T 300 s 3 3.33 0 Hz The frequency

More information

Unit 14 Harmonic Motion. Your Comments

Unit 14 Harmonic Motion. Your Comments Today s Concepts: Periodic Motion Siple - Mass on spring Daped Forced Resonance Siple - Pendulu Unit 1, Slide 1 Your Coents Please go through the three equations for siple haronic otion and phase angle

More information

PH 221-1D Spring Oscillations. Lectures Chapter 15 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition)

PH 221-1D Spring Oscillations. Lectures Chapter 15 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) PH 1-1D Spring 013 Oscillations Lectures 35-37 Chapter 15 (Halliday/Resnick/Walker, Fundaentals of Physics 9 th edition) 1 Chapter 15 Oscillations In this chapter we will cover the following topics: Displaceent,

More information

Physics 2210 Fall smartphysics 20 Conservation of Angular Momentum 21 Simple Harmonic Motion 11/23/2015

Physics 2210 Fall smartphysics 20 Conservation of Angular Momentum 21 Simple Harmonic Motion 11/23/2015 Physics 2210 Fall 2015 sartphysics 20 Conservation of Angular Moentu 21 Siple Haronic Motion 11/23/2015 Exa 4: sartphysics units 14-20 Midter Exa 2: Day: Fri Dec. 04, 2015 Tie: regular class tie Section

More information

Name Period. What force did your partner s exert on yours? Write your answer in the blank below:

Name Period. What force did your partner s exert on yours? Write your answer in the blank below: Nae Period Lesson 7: Newton s Third Law and Passive Forces 7.1 Experient: Newton s 3 rd Law Forces of Interaction (a) Tea up with a partner to hook two spring scales together to perfor the next experient:

More information

26 Impulse and Momentum

26 Impulse and Momentum 6 Ipulse and Moentu First, a Few More Words on Work and Energy, for Coparison Purposes Iagine a gigantic air hockey table with a whole bunch of pucks of various asses, none of which experiences any friction

More information

m A 9. The length of a simple pendulum with a period on Earth of one second is most nearly (A) 0.12 m (B) 0.25 m (C) 0.50 m (D) 1.0 m (E) 10.

m A 9. The length of a simple pendulum with a period on Earth of one second is most nearly (A) 0.12 m (B) 0.25 m (C) 0.50 m (D) 1.0 m (E) 10. P Physics Multiple Choice Practice Oscillations. ass, attache to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu isplaceent fro its equilibriu position is. What

More information

PHYSICS - CLUTCH CH 05: FRICTION, INCLINES, SYSTEMS.

PHYSICS - CLUTCH CH 05: FRICTION, INCLINES, SYSTEMS. !! www.clutchprep.co INTRO TO FRICTION Friction happens when two surfaces are in contact f = μ =. KINETIC FRICTION (v 0 *): STATIC FRICTION (v 0 *): - Happens when ANY object slides/skids/slips. * = Point

More information

8.1 Force Laws Hooke s Law

8.1 Force Laws Hooke s Law 8.1 Force Laws There are forces that don't change appreciably fro one instant to another, which we refer to as constant in tie, and forces that don't change appreciably fro one point to another, which

More information

PHY 140Y FOUNDATIONS OF PHYSICS Tutorial Questions #9 Solutions November 12/13

PHY 140Y FOUNDATIONS OF PHYSICS Tutorial Questions #9 Solutions November 12/13 PHY 4Y FOUNDAIONS OF PHYSICS - utorial Questions #9 Solutions Noveber /3 Conservation of Ener and Sprins. One end of a assless sprin is placed on a flat surface, with the other end pointin upward, as shown

More information

CE573 Structural Dynamics [Fall 2008]

CE573 Structural Dynamics [Fall 2008] CE573 Structural Dynaics [Fall 2008] 1) A rigid vehicle weighing 2000 lb, oving horizontally at a velocity of 12 ft/sec, is stopped by a barrier consisting of wire ropes stretched between two rigid anchors

More information

15 Newton s Laws #2: Kinds of Forces, Creating Free Body Diagrams

15 Newton s Laws #2: Kinds of Forces, Creating Free Body Diagrams Chapter 15 ewton s Laws #2: inds of s, Creating ree Body Diagras 15 ewton s Laws #2: inds of s, Creating ree Body Diagras re is no force of otion acting on an object. Once you have the force or forces

More information

Definition of Work, The basics

Definition of Work, The basics Physics 07 Lecture 16 Lecture 16 Chapter 11 (Work) v Eploy conservative and non-conservative forces v Relate force to potential energy v Use the concept of power (i.e., energy per tie) Chapter 1 v Define

More information

Physics 120 Final Examination

Physics 120 Final Examination Physics 120 Final Exaination 12 August, 1998 Nae Tie: 3 hours Signature Calculator and one forula sheet allowed Student nuber Show coplete solutions to questions 3 to 8. This exaination has 8 questions.

More information

Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world

Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Pearson Education Liited Edinburgh Gate Harlow Esse CM0 JE England and Associated Copanies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk Pearson Education Liited 04 All rights

More information

Work, Energy and Momentum

Work, Energy and Momentum Work, Energy and Moentu Work: When a body oves a distance d along straight line, while acted on by a constant force of agnitude F in the sae direction as the otion, the work done by the force is tered

More information

NAME NUMBER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002. PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2 Q2 Q3 Total 40%

NAME NUMBER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002. PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2 Q2 Q3 Total 40% NAME NUMER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002 PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2.5 Q1 ( ) 2 Q2 Q3 Total 40% Use the followings: Magnitude of acceleration due to gravity

More information

SIMPLE HARMONIC MOTION: NEWTON S LAW

SIMPLE HARMONIC MOTION: NEWTON S LAW SIMPLE HARMONIC MOTION: NEWTON S LAW siple not siple PRIOR READING: Main 1.1, 2.1 Taylor 5.1, 5.2 http://www.yoops.org/twocw/it/nr/rdonlyres/physics/8-012fall-2005/7cce46ac-405d-4652-a724-64f831e70388/0/chp_physi_pndul.jpg

More information

USEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS. By: Ian Blokland, Augustana Campus, University of Alberta

USEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS. By: Ian Blokland, Augustana Campus, University of Alberta 1 USEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS By: Ian Bloland, Augustana Capus, University of Alberta For: Physics Olypiad Weeend, April 6, 008, UofA Introduction: Physicists often attept to solve

More information

1B If the stick is pivoted about point P a distance h = 10 cm from the center of mass, the period of oscillation is equal to (in seconds)

1B If the stick is pivoted about point P a distance h = 10 cm from the center of mass, the period of oscillation is equal to (in seconds) 05/07/03 HYSICS 3 Exa #1 Use g 10 /s in your calculations. NAME Feynan lease write your nae also on the back side of this exa 1. 1A A unifor thin stick of ass M 0. Kg and length 60 c is pivoted at one

More information

F = 0. x o F = -k x o v = 0 F = 0. F = k x o v = 0 F = 0. x = 0 F = 0. F = -k x 1. PHYSICS 151 Notes for Online Lecture 2.4.

F = 0. x o F = -k x o v = 0 F = 0. F = k x o v = 0 F = 0. x = 0 F = 0. F = -k x 1. PHYSICS 151 Notes for Online Lecture 2.4. PHYSICS 151 Notes for Online Lecture.4 Springs, Strings, Pulleys, and Connected Objects Hook s Law F = 0 F = -k x 1 x = 0 x = x 1 Let s start with a horizontal spring, resting on a frictionless table.

More information

PHYS 102 Previous Exam Problems

PHYS 102 Previous Exam Problems PHYS 102 Previous Exa Probles CHAPTER 16 Waves Transverse waves on a string Power Interference of waves Standing waves Resonance on a string 1. The displaceent of a string carrying a traveling sinusoidal

More information

Application of Newton s Laws. F fr

Application of Newton s Laws. F fr Application of ewton Law. A hocey puc on a frozen pond i given an initial peed of 0.0/. It lide 5 before coing to ret. Deterine the coefficient of inetic friction ( μ between the puc and ice. The total

More information

Vector Spaces in Physics 8/6/2015. Chapter 4. Practical Examples.

Vector Spaces in Physics 8/6/2015. Chapter 4. Practical Examples. Vector Spaces in Physics 8/6/15 Chapter 4. Practical Exaples. In this chapter we will discuss solutions to two physics probles where we ae use of techniques discussed in this boo. In both cases there are

More information

In the session you will be divided into groups and perform four separate experiments:

In the session you will be divided into groups and perform four separate experiments: Mechanics Lab (Civil Engineers) Nae (please print): Tutor (please print): Lab group: Date of lab: Experients In the session you will be divided into groups and perfor four separate experients: (1) air-track

More information

EN40: Dynamics and Vibrations. Final Examination Tuesday May 15, 2011

EN40: Dynamics and Vibrations. Final Examination Tuesday May 15, 2011 EN40: ynaics and Vibrations Final Exaination Tuesday May 15, 011 School of Engineering rown University NME: General Instructions No collaboration of any ind is peritted on this exaination. You ay use double

More information

1 k. 1 m. m A. AP Physics Multiple Choice Practice Work-Energy

1 k. 1 m. m A. AP Physics Multiple Choice Practice Work-Energy AP Physics Multiple Choice Practice Wor-Energy 1. A ass attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is

More information

Chapter 13. Simple Harmonic Motion

Chapter 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 information

Systems of Masses. 1. Ignoring friction, calculate the acceleration of the system below and the tension in the rope. and (4.0)(9.80) 39.

Systems of Masses. 1. Ignoring friction, calculate the acceleration of the system below and the tension in the rope. and (4.0)(9.80) 39. Systes of Masses. Ignoring friction, calculate the acceleration of the syste below and the tension in the rope. Drawing individual free body diagras we get 4.0kg 7.0kg g 9.80 / s a?? g and g (4.0)(9.80)

More information

Physics 201 Lecture 29

Physics 201 Lecture 29 Phsics 1 ecture 9 Goals ecture 9 v Describe oscillator otion in a siple pendulu v Describe oscillator otion with torques v Introduce daping in SHM v Discuss resonance v Final Ea Details l Sunda, Ma 13th

More information

(b) Frequency is simply the reciprocal of the period: f = 1/T = 2.0 Hz.

(b) Frequency is simply the reciprocal of the period: f = 1/T = 2.0 Hz. Chapter 5. (a) During siple haronic otion, the speed is (oentarily) zero when the object is at a turning point (that is, when x = +x or x = x ). Consider that it starts at x = +x and we are told that t

More information

Chapter 5, Conceptual Questions

Chapter 5, Conceptual Questions Chapter 5, Conceptual Questions 5.1. Two forces are present, tension T in the cable and gravitational force 5.. F G as seen in the figure. Four forces act on the block: the push of the spring F, sp gravitational

More information

dt dt THE AIR TRACK (II)

dt dt THE AIR TRACK (II) THE AIR TRACK (II) References: [] The Air Track (I) - First Year Physics Laoratory Manual (PHY38Y and PHYY) [] Berkeley Physics Laoratory, nd edition, McGraw-Hill Book Copany [3] E. Hecht: Physics: Calculus,

More information

JOURNAL OF PHYSICAL AND CHEMICAL SCIENCES

JOURNAL OF PHYSICAL AND CHEMICAL SCIENCES JOURNAL OF PHYSIAL AND HEMIAL SIENES Journal hoepage: http://scienceq.org/journals/jps.php Review Open Access A Review of Siple Haronic Motion for Mass Spring Syste and Its Analogy to the Oscillations

More information

ma x = -bv x + F rod.

ma x = -bv x + F rod. Notes on Dynaical Systes Dynaics is the study of change. The priary ingredients of a dynaical syste are its state and its rule of change (also soeties called the dynaic). Dynaical systes can be continuous

More information

Transverse waves. Waves. Wave motion. Electromagnetic Spectrum EM waves are transverse.

Transverse waves. Waves. Wave motion. Electromagnetic Spectrum EM waves are transverse. Transerse waes Physics Enhanceent Prograe for Gifted Students The Hong Kong Acadey for Gifted Education and, HKBU Waes. Mechanical waes e.g. water waes, sound waes, seisic waes, strings in usical instruents.

More information

XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K. https://promotephysics.wordpress.com

XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K. https://promotephysics.wordpress.com XI PHYSICS M. AFFAN KHAN LECTURER PHYSICS, AKHSS, K affan_414@live.co https://prootephysics.wordpress.co [MOTION] CHAPTER NO. 3 In this chapter we are going to discuss otion in one diension in which we

More information

SRI LANKAN PHYSICS OLYMPIAD MULTIPLE CHOICE TEST 30 QUESTIONS ONE HOUR AND 15 MINUTES

SRI LANKAN PHYSICS OLYMPIAD MULTIPLE CHOICE TEST 30 QUESTIONS ONE HOUR AND 15 MINUTES SRI LANKAN PHYSICS OLYMPIAD - 5 MULTIPLE CHOICE TEST QUESTIONS ONE HOUR AND 5 MINUTES INSTRUCTIONS This test contains ultiple choice questions. Your answer to each question ust be arked on the answer sheet

More information

Department of Physics Preliminary Exam January 3 6, 2006

Department of Physics Preliminary Exam January 3 6, 2006 Departent of Physics Preliinary Exa January 3 6, 2006 Day 1: Classical Mechanics Tuesday, January 3, 2006 9:00 a.. 12:00 p.. Instructions: 1. Write the answer to each question on a separate sheet of paper.

More information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY OF SASKATCHEWAN Departent of Physics and Engineering Physics 017 Saskatchewan High School Physics Scholarship Copetition Wednesday May 10, 017 Tie allowed: 90 inutes This copetition is based

More information

Physics 20 Lesson 28 Simple Harmonic Motion Dynamics & Energy

Physics 20 Lesson 28 Simple Harmonic Motion Dynamics & Energy Phyic 0 Leon 8 Siple Haronic Motion Dynaic & Energy Now that we hae learned about work and the Law of Coneration of Energy, we are able to look at how thee can be applied to the ae phenoena. In general,

More information

Newton's Laws. Lecture 2 Key Concepts. Newtonian mechanics and relation to Kepler's laws The Virial Theorem Tidal forces Collision physics

Newton's Laws. Lecture 2 Key Concepts. Newtonian mechanics and relation to Kepler's laws The Virial Theorem Tidal forces Collision physics Lecture 2 Key Concepts Newtonian echanics and relation to Kepler's laws The Virial Theore Tidal forces Collision physics Newton's Laws 1) An object at rest will reain at rest and an object in otion will

More information

In this chapter we will start the discussion on wave phenomena. We will study the following topics:

In this chapter we will start the discussion on wave phenomena. We will study the following topics: Chapter 16 Waves I In this chapter we will start the discussion on wave phenoena. We will study the following topics: Types of waves Aplitude, phase, frequency, period, propagation speed of a wave Mechanical

More information

Page 1. Physics 131: Lecture 16. Today s Agenda. Collisions. Elastic Collision

Page 1. Physics 131: Lecture 16. Today s Agenda. Collisions. Elastic Collision Physics 131: Lecture 16 Today s Agenda Elastic Collisions Definition Exaples Work and Energy Definition of work Exaples Physics 01: Lecture 10, Pg 1 Collisions Moentu is alost always consered during as

More information

= 1.49 m/s m. 2 kg. 2 kg

= 1.49 m/s m. 2 kg. 2 kg 5.6. Visualize: Please refer to Figure Ex5.6. Solve: For the diagra on the left, three of the vectors lie along the axes of the tilted coordinate sste. Notice that the angle between the 3 N force and the

More information

Oscillations. PHYS 101 Previous Exam Problems CHAPTER. Simple harmonic motion Mass-spring system Energy in SHM Pendulums

Oscillations. 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 information

NB1140: Physics 1A - Classical mechanics and Thermodynamics Problem set 2 - Forces and energy Week 2: November 2016

NB1140: Physics 1A - Classical mechanics and Thermodynamics Problem set 2 - Forces and energy Week 2: November 2016 NB1140: Physics 1A - Classical echanics and Therodynaics Proble set 2 - Forces and energy Week 2: 21-25 Noveber 2016 Proble 1. Why force is transitted uniforly through a assless string, a assless spring,

More information

1 (40) Gravitational Systems Two heavy spherical (radius 0.05R) objects are located at fixed positions along

1 (40) Gravitational Systems Two heavy spherical (radius 0.05R) objects are located at fixed positions along (40) Gravitational Systes Two heavy spherical (radius 0.05) objects are located at fixed positions along 2M 2M 0 an axis in space. The first ass is centered at r = 0 and has a ass of 2M. The second ass

More information

Chapter 14 Oscillations. Copyright 2009 Pearson Education, Inc.

Chapter 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 information