Experiment Type: Open-Ended

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Experiment Type: Open-Ended"

Transcription

1 Simple Harmonic Oscillation Overview Experiment Type: Open-Ended In this experiment, students will look at three kinds of oscillators and determine whether or not they can be approximated as simple harmonic oscillators. Students should determine under what conditions they can be characterized as simple harmonic oscillators. Students should also determine if the oscillation is damped over time. Key Concepts Oscillators, oscillations, simple harmonic oscillation, damped linear oscillation, damping constant, spring constant, spring frequency Objectives On completion of this experiment, students should be able to: 1) explain the concept of simple harmonic motion 2) determine if an oscillation is simple harmonic or not 3) determine the frequency of oscillations 4) explain the concept of damped oscillations Review of Concepts Oscillations An oscillation is a back and forth motion. You can see oscillations all around you every day. It is the swaying of the fronds in a palm tree, the rocking of a rocking chair, the ticking of a grandfather clock, the motion of the suspension in your car, the swinging of a child in a playground. Sometimes we want to have oscillations (in rocking chairs, swings, etc.), other times we do not (in buildings, cars, etc.). In order to build things as scientists and engineers, we need to understand oscillations. Why do things oscillate? What are the properties of oscillations? The conditions you need in order for an object to oscillate are: the object must be under the influence of a net restoring force there must be at least one equilibrium position An equilibrium position is a location in space where the object has no net force operating on it. A restoring force is a force which points in the direction of (or along the path to) the equilibrium position. In other words, the restoring force tries to return the object to the equilibrium position. Simple Harmonic Oscillation

2 The simplest kind of oscillation is the simple harmonic oscillation. It is the simplest because the restoring force can be characterized as proportional to the displacement, i.e. r r = kx (9-1) In this equation, k is a constant of proportionality, usually called the spring constant, and x r is a displacement. Note that the displacement need not be in the x direction, but can be a displacement along a path (I will give you an example shortly). Now having said this, let me tell you that there are very few real, net restoring forces which can be characterized with this formula exactly. In fact, I can think of none. I know what you re thinking. You re thinking But, but That s the spring force, Hooke s Law, I learned about in my text Well, yes, Eq. (9-1) is Hooke s Law. That makes sense, because you already know that springs oscillate very readily. The question is how well does Hooke s Law describe a spring? What happens if you stretch a real spring too much? (Haven t you ever ruined a Slinky?) Does it have the same springiness after you do this? The answer is that there is a region of displacements for which a spring will follow Hooke s Law fairly reasonably. Beyond that and the spring will experience a process called hysteresis. (That is a topic for another course, however.) Many restoring forces can be approximated as Eq. (9-1) under certain conditions. In your experiment today, you are going to look at a few examples of oscillators and you will tell me if the oscillator can be approximated as a simple harmonic oscillator and if so, under what conditions is it approximately simple harmonic. Let me give you an example other than the simple spring-mass system that you can find in your book. Figure -1 A mass sliding in a frictionless, circular bowl This is clearly an oscillator. If you move the mass to any side of the bowl, it will slosh back and forth. But is it a simple harmonic oscillator? To answer this question, let s draw the free body diagram.

3 Figure -2 The free body diagram of the sliding mass in the frictionless bowl This is an example of an oscillator whose restoring force acts along the path of motion, in this case, along the surface of the bowl. The restoring force in this case is the component of the gravitational force which acts along the surface of the bowl. = mg sin (9-2) Well, that doesn t look like Hooke s Law at all So this is not a simple harmonic oscillator in general. However, for small angles, sin θ θ. Also, the displacement r r along the path is related to θ by the formula = s / R. That means that for small angles this restoring force becomes = mg' & = mg$ % s R " (9-3) Eq. (9-3) has the form F = (constant)*displacement. The spring constant in this case is mg/r. So for small angles, this mass sliding in a frictionless bowl is a simple harmonic oscillator That s all well and good for theoretical determinations, but how do we find out if the oscillator is simple harmonic experimentally? To find out experimentally, we need to know the equation of motion for an object undergoing simple harmonic motion. The equation of motion for simple harmonic oscillation is a cosine function. x t) = Acos( " t + ) (9-4) ( In this equation, A is the (constant) amplitude of the oscillation, ω is the frequency of the oscillation, and δ o is the initial phase of the oscillation. Be careful X(t) is the distance along the path of the motion That means the arc distance, s, in the case of the mass sliding in the bowl. The frequency of the oscillation for simple harmonic motion is

4 k = (9-5) m If you can verify both (9-4) and (9-5) are true for your system, then you have successfully shown that the oscillator can be approximated as a simple harmonic oscillator. Damped Oscillations Of course, there s no such thing as a perfectly lossless mechanical system. If we were to look at a real spring oscillating over some period of time, the graph of its motion would never be a perfect cosine function. After a while, the oscillations would die down. In other words, the oscillator would lose energy over time. A force which causes the oscillator to lose energy is called a damping force. Some common damping forces are friction and air drag. Since we have already discussed friction in a previous lab, I will be very brief. Sometimes the damping force can be modeled as proportional to the velocity of the mass, i.e. F damping = bv (9-6) where b is a constant of proportionality called the damping constant. When this is true, the equation of motion becomes a sinusoidal function which is attenuated by a decreasing exponential, Figure -3 A plot of the displacement vs. time of a damped harmonic oscillator ( b / 2m) t x ( t) = Ae cos( "' t + ) o (9-7) The frequency is changed from the natural frequency (the frequency for simple harmonic oscillation) by the relation

5 (' = ( & 1' $ % 2 ( " b m 2 (9-8) For small damping forces, this shift in the frequency is very small, so equation (9-8) is not very helpful for most cases. It is sufficient that you show that the motion of your oscillator is Eq. (9-7) in form. Procedure You will come up with a procedure in your group Read the task (below) carefully and come up with a procedure that you think will accomplish it. You have two weeks to complete this task. Your task: You need to determine whether or not each of the oscillators you have chosen can be approximately described as a simple harmonic oscillator. This means you must determine: o Under what conditions it can be described as such. (E.g. small timescale, small oscillations, etc.). Please don t test extreme amplitudes in the spring-mass system; it may damage the spring o What parameters describe the motion. For example, what determines the frequency of oscillation in each system? o Whether or not each of the oscillators is damped over time. The spring has an added parameter: the effective mass. This will be discussed in class during the 2 nd week. You must pick three oscillators to investigate. You only need to fully complete the task for the first two. The last one may prove unreasonable to model. One of your oscillators must be a simple spring mass system. Choose either a mass hanging on a spring vertically or a mass attached to a spring horizontally. There are many different sets of equipment you can use for the horizontal case (an air track, a car track, etc.) One of your oscillators must be a simple pendulum (a mass on a string). The last oscillator can be anything you can dream up with the equipment we have. I challenge you to come up with something that is very non-linear (I.e. something that cannot be approximated well as a simple harmonic oscillator). For this last case, all you need to do is find the position as a function of time, rather than analyzing it carefully. Think of something wacky the wackier the better Two springs attached to a single mass diagonally and bouncing on a table? Pendulums attached to pendulums? Have fun with this last one

Simple Harmonic Motion Concepts

Simple Harmonic Motion Concepts Simple Harmonic Motion Concepts INTRODUCTION Have you ever wondered why a grandfather clock keeps accurate time? The motion of the pendulum is a particular kind of repetitive or periodic motion called

More information

Periodic Motion or Oscillations. Physics 232 Lecture 01 1

Periodic Motion or Oscillations. Physics 232 Lecture 01 1 Periodic Motion or Oscillations Physics 3 Lecture 01 1 Periodic Motion Periodic Motion is motion that repeats about a point of stable equilibrium Stable Equilibrium Unstable Equilibrium A necessary requirement

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Harmonic Motion Restating Hooke s law The equation of motion Phase, frequency, amplitude Simple Pendulum Damped and Forced oscillations Resonance Harmonic Motion A lot of motion in the real world

More information

AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false?

AP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The

More information

Hooke s Law. Spring. Simple Harmonic Motion. Energy. 12/9/09 Physics 201, UW-Madison 1

Hooke s Law. Spring. Simple Harmonic Motion. Energy. 12/9/09 Physics 201, UW-Madison 1 Hooke s Law Spring Simple Harmonic Motion Energy 12/9/09 Physics 201, UW-Madison 1 relaxed position F X = -kx > 0 F X = 0 x apple 0 x=0 x > 0 x=0 F X = - kx < 0 x 12/9/09 Physics 201, UW-Madison 2 We know

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Harmonic Motion 1 Object To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2 Apparatus Assorted weights

More information

Lab M1: The Simple Pendulum

Lab M1: The Simple Pendulum Lab M1: The Simple Pendulum Introduction. The simple pendulum is a favorite introductory exercise because Galileo's experiments on pendulums in the early 1600s are usually regarded as the beginning of

More information

LABORATORY 9. Simple Harmonic Motion

LABORATORY 9. Simple Harmonic Motion LABORATORY 9 Simple Harmonic Motion Purpose In this experiment we will investigate two examples of simple harmonic motion: the mass-spring system and the simple pendulum. For the mass-spring system we

More information

Physics 53. Oscillations. You've got to be very careful if you don't know where you're going, because you might not get there.

Physics 53. Oscillations. You've got to be very careful if you don't know where you're going, because you might not get there. Physics 53 Oscillations You've got to be very careful if you don't know where you're going, because you might not get there. Yogi Berra Overview Many natural phenomena exhibit motion in which particles

More information

A ball, attached to a cord of length 1.20 m, is set in motion so that it is swinging backwards and forwards like a pendulum.

A ball, attached to a cord of length 1.20 m, is set in motion so that it is swinging backwards and forwards like a pendulum. MECHANICS: SIMPLE HARMONIC MOTION QUESTIONS THE PENDULUM (2014;2) A pendulum is set up, as shown in the diagram. The length of the cord attached to the bob is 1.55 m. The bob has a mass of 1.80 kg. The

More information

Lecture Presentation Chapter 14 Oscillations

Lecture Presentation Chapter 14 Oscillations Lecture Presentation Chapter 14 Oscillations Suggested Videos for Chapter 14 Prelecture Videos Describing Simple Harmonic Motion Details of SHM Damping and Resonance Class Videos Oscillations Basic Oscillation

More information

Simple Harmonic Motion

Simple Harmonic Motion Periodic motion Earth around the sun Elastic ball bouncing up an down Quartz in your watch, computer clock, ipod clock, etc. Heart beat, and many more In taking your pulse, you count 70.0 heartbeats in

More information

Chapter 14. Oscillations. PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition Pearson Education, Inc.

Chapter 14. Oscillations. PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition Pearson Education, Inc. Chapter 14 Oscillations PowerPoint Lectures for College Physics: A Strategic Approach, Second Edition 14 Oscillations Reading Quiz 1. The type of function that describes simple harmonic motion is A.

More information

Hooke s Law and Simple Harmonic Motion

Hooke s Law and Simple Harmonic Motion Hooke s Law and Simple Harmonic Motion OBJECTIVE to measure the spring constant of the springs using Hooke s Law to explore the static properties of springy objects and springs, connected in series and

More information

1 of 10 11/23/2009 6:37 PM

1 of 10 11/23/2009 6:37 PM hapter 14 Homework Due: 9:00am on Thursday November 19 2009 Note: To understand how points are awarded read your instructor's Grading Policy. [Return to Standard Assignment View] Good Vibes: Introduction

More information

Spring Simple Harmonic Oscillator. Spring constant. Potential Energy stored in a Spring. Understanding oscillations. Understanding oscillations

Spring Simple Harmonic Oscillator. Spring constant. Potential Energy stored in a Spring. Understanding oscillations. Understanding oscillations Spring Simple Harmonic Oscillator Simple Harmonic Oscillations and Resonance We have an object attached to a spring. The object is on a horizontal frictionless surface. We move the object so the spring

More information

Prelab Exercises: Hooke's Law and the Behavior of Springs

Prelab Exercises: Hooke's Law and the Behavior of Springs 59 Prelab Exercises: Hooke's Law and the Behavior of Springs Study the description of the experiment that follows and answer the following questions.. (3 marks) Explain why a mass suspended vertically

More information

Oscillations. The Force. The Motion

Oscillations. The Force. The Motion Team Oscillations Oscillatory motion is motion that repeats itself. An object oscillates if it moves back and forth along a fixed path between two extreme positions. Oscillations are everywhere in the

More information

Name: Lab Partner: Section:

Name: Lab Partner: Section: Chapter 10 Simple Harmonic Motion Name: Lab Partner: Section: 10.1 Purpose Simple harmonic motion will be examined in this experiment. 10.2 Introduction A periodic motion is one that repeats itself in

More information

Physics 231 Lecture 15

Physics 231 Lecture 15 Physics 31 ecture 15 Main points of today s lecture: Simple harmonic motion Mass and Spring Pendulum Circular motion T 1/f; f 1/ T; ω πf for mass and spring ω x Acos( ωt) v ωasin( ωt) x ax ω Acos( ωt)

More information

THE NOT SO SIMPLE PENDULUM

THE NOT SO SIMPLE PENDULUM INTRODUCTION: THE NOT SO SIMPLE PENDULUM This laboratory experiment is used to study a wide range of topics in mechanics like velocity, acceleration, forces and their components, the gravitational force,

More information

Updated 2013 (Mathematica Version) M1.1. Lab M1: The Simple Pendulum

Updated 2013 (Mathematica Version) M1.1. Lab M1: The Simple Pendulum Updated 2013 (Mathematica Version) M1.1 Introduction. Lab M1: The Simple Pendulum The simple pendulum is a favorite introductory exercise because Galileo's experiments on pendulums in the early 1600s are

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Harmonic Motion Simple harmonic motion is one of the most common motions found in nature and can be observed from the microscopic vibration of atoms in a solid to rocking of a supertanker on the

More information

PENDULUM PERIODS. First Last. Partners: student1, student2, and student3

PENDULUM PERIODS. First Last. Partners: student1, student2, and student3 PENDULUM PERIODS First Last Partners: student1, student2, and student3 Governor s School for Science and Technology 520 Butler Farm Road, Hampton, VA 23666 April 13, 2011 ABSTRACT The effect of amplitude,

More information

AP Physics C. Oscillations/SHM Review Packet

AP Physics C. Oscillations/SHM Review Packet AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete

More information

Lab 5: Conservation of Energy

Lab 5: Conservation of Energy Lab 5: Conservation of Energy Equipment SWS, 1-meter stick, 2-meter stick, heavy duty bench clamp, 90-cm rod, 40-cm rod, 2 double clamps, brass spring, 100-g mass, 500-g mass with 5-cm cardboard square

More information

Simple Harmonic Motion(SHM) Period and Frequency. Period and Frequency. Cosines and Sines

Simple Harmonic Motion(SHM) Period and Frequency. Period and Frequency. Cosines and Sines Simple Harmonic Motion(SHM) Vibration (oscillation) Equilibrium position position of the natural length of a spring Amplitude maximum displacement Period and Frequency Period (T) Time for one complete

More information

SIMPLE HARMONIC MOTION

SIMPLE HARMONIC MOTION SIMPLE HARMONIC MOTION PURPOSE The purpose of this experiment is to investigate one of the fundamental types of motion that exists in nature - simple harmonic motion. The importance of this kind of motion

More information

PHYS 202 Laboratory #4. Activity 1: Thinking about Oscillating Systems

PHYS 202 Laboratory #4. Activity 1: Thinking about Oscillating Systems SHM Lab 1 Introduction PHYS 202 Laboratory #4 Oscillations and Simple Harmonic Motion In this laboratory, we examine three simple oscillatory systems: a mass on a spring, a pendulum, and a mass on a rubber

More information

HOOKE S LAW AND OSCILLATIONS

HOOKE S LAW AND OSCILLATIONS 9 HOOKE S LAW AND OSCILLATIONS OBJECTIVE To measure the effect of amplitude, mass, and spring constant on the period of a spring-mass oscillator. INTRODUCTION The force which restores a spring to its equilibrium

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Harmonic Motion Objective: In this exercise you will investigate the simple harmonic motion of mass suspended from a helical (coiled) spring. Apparatus: Spring 1 Table Post 1 Short Rod 1 Right-angled

More information

Oscillations: Mass on a Spring and Pendulums

Oscillations: Mass on a Spring and Pendulums Chapter 3 Oscillations: Mass on a Spring and Pendulums 3.1 Purpose 3.2 Introduction Galileo is said to have been sitting in church watching the large chandelier swinging to and fro when he decided that

More information

Advanced Higher Physics: MECHANICS. Simple Harmonic Motion

Advanced Higher Physics: MECHANICS. Simple Harmonic Motion Advanced Higher Physics: MECHANICS Simple Harmonic Motion At the end of this section, you should be able to: Describe examples of simple harmonic motion (SHM). State that in SHM the unbalanced force is

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Harmonic Motion 9M Object: Apparatus: To determine the force constant of a spring and then study the harmonic motion of that spring when it is loaded with a mass m. Force sensor, motion sensor,

More information

physics 111N oscillations & waves

physics 111N oscillations & waves physics 111N oscillations & waves periodic motion! often a physical system will repeat the same motion over and over! we call this periodic motion, or an oscillation the time it takes for the motion to

More information

Chapter 1. Oscillations. Oscillations

Chapter 1. Oscillations. Oscillations Oscillations 1. A mass m hanging on a spring with a spring constant k has simple harmonic motion with a period T. If the mass is doubled to 2m, the period of oscillation A) increases by a factor of 2.

More information

Practice Test SHM with Answers

Practice Test SHM with Answers Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one

More information

SIMPLE HARMONIC MOTION: SHIFTED ORIGIN AND PHASE

SIMPLE HARMONIC MOTION: SHIFTED ORIGIN AND PHASE MISN-0-26 SIMPLE HARMONIC MOTION: SHIFTED ORIGIN AND PHASE SIMPLE HARMONIC MOTION: SHIFTED ORIGIN AND PHASE by Kirby Morgan 1. Dynamics of Harmonic Motion a. Force Varies in Magnitude and Direction................

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Harmonic Motion -Theory Simple harmonic motion refers to the periodic sinusoidal oscillation of an object or quantity. Simple harmonic motion is eecuted by any quantity obeying the Differential

More information

EXPERIMENT 2 Measurement of g: Use of a simple pendulum

EXPERIMENT 2 Measurement of g: Use of a simple pendulum EXPERIMENT 2 Measurement of g: Use of a simple pendulum OBJECTIVE: To measure the acceleration due to gravity using a simple pendulum. Textbook reference: pp10-15 INTRODUCTION: Many things in nature wiggle

More information

Solving the Harmonic Oscillator Equation. Morgan Root NCSU Department of Math

Solving the Harmonic Oscillator Equation. Morgan Root NCSU Department of Math Solving the Harmonic Oscillator Equation Morgan Root NCSU Department of Math Spring-Mass System Consider a mass attached to a wall by means of a spring. Define y to be the equilibrium position of the block.

More information

Experiment 4: Harmonic Motion Analysis

Experiment 4: Harmonic Motion Analysis Experiment 4: Harmonic Motion Analysis Background In this experiment you will investigate the influence of damping on a driven harmonic oscillator and study resonant conditions. The following theoretical

More information

Chapter 13, example problems: x (cm) 10.0

Chapter 13, example problems: x (cm) 10.0 Chapter 13, example problems: (13.04) Reading Fig. 13-30 (reproduced on the right): (a) Frequency f = 1/ T = 1/ (16s) = 0.0625 Hz. (since the figure shows that T/2 is 8 s.) (b) The amplitude is 10 cm.

More information

PHYS 2425 Engineering Physics I EXPERIMENT 9 SIMPLE HARMONIC MOTION

PHYS 2425 Engineering Physics I EXPERIMENT 9 SIMPLE HARMONIC MOTION PHYS 2425 Engineering Physics I EXPERIMENT 9 SIMPLE HARMONIC MOTION I. INTRODUCTION The objective of this experiment is the study of oscillatory motion. In particular the springmass system and the simple

More information

Up and Down: Damped Harmonic Motion

Up and Down: Damped Harmonic Motion Up and Down: Damped Harmonic Motion Activity 27 An object hanging from a spring can bounce up and down in a simple way. The vertical position of the object can be described mathematically in terms of a

More information

Type: Double Date: Simple Harmonic Motion III. Homework: Read 10.3, Do CONCEPT QUEST #(7) Do PROBLEMS #(5, 19, 28) Ch. 10

Type: Double Date: Simple Harmonic Motion III. Homework: Read 10.3, Do CONCEPT QUEST #(7) Do PROBLEMS #(5, 19, 28) Ch. 10 Type: Double Date: Objective: Simple Harmonic Motion II Simple Harmonic Motion III Homework: Read 10.3, Do CONCEPT QUEST #(7) Do PROBLEMS #(5, 19, 28) Ch. 10 AP Physics B Mr. Mirro Simple Harmonic Motion

More information

Determination of Acceleration due to Gravity

Determination of Acceleration due to Gravity Experiment 2 24 Kuwait University Physics 105 Physics Department Determination of Acceleration due to Gravity Introduction In this experiment the acceleration due to gravity (g) is determined using two

More information

both double. A. T and v max B. T remains the same and v max doubles. both remain the same. C. T and v max

both double. A. T and v max B. T remains the same and v max doubles. both remain the same. C. T and v max Q13.1 An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object s maximum speed

More information

MECHANICS IV - SIMPLE HARMONIC MOTION

MECHANICS IV - SIMPLE HARMONIC MOTION M-IV-p.1 A. OSCILLATIONS B. SIMPLE PENDULUM C. KINEMATICS OF SIMPLE HARMONIC MOTION D. SPRING-AND-MASS SYSTEM E. ENERGY OF SHM F. DAMPED HARMONIC MOTION G. FORCED VIBRATION A. OSCILLATIONS A to-and-fro

More information

HOOKE'S LAW AND SIMPLE HARMONIC MOTION OBJECT

HOOKE'S LAW AND SIMPLE HARMONIC MOTION OBJECT 5 M19 M19.1 HOOKE'S LAW AND SIMPLE HARMONIC MOTION OBJECT The object of this experiment is to determine whether a vertical mass-spring system obeys Hooke's Law and to study simple harmonic motion. THEORY

More information

1.10 Using Figure 1.6, verify that equation (1.10) satisfies the initial velocity condition. t + ") # x (t) = A! n. t + ") # v(0) = A!

1.10 Using Figure 1.6, verify that equation (1.10) satisfies the initial velocity condition. t + ) # x (t) = A! n. t + ) # v(0) = A! 1.1 Using Figure 1.6, verify that equation (1.1) satisfies the initial velocity condition. Solution: Following the lead given in Example 1.1., write down the general expression of the velocity by differentiating

More information

People s Physics book 3e Ch 25-1

People s Physics book 3e Ch 25-1 The Big Idea: In most realistic situations forces and accelerations are not fixed quantities but vary with time or displacement. In these situations algebraic formulas cannot do better than approximate

More information

= mg [down] =!mg [up]; F! x

= mg [down] =!mg [up]; F! x Section 4.6: Elastic Potential Energy and Simple Harmonic Motion Mini Investigation: Spring Force, page 193 Answers may vary. Sample answers: A. The relationship between F g and x is linear. B. The slope

More information

Simple Pendulum 10/10

Simple Pendulum 10/10 Physical Science 101 Simple Pendulum 10/10 Name Partner s Name Purpose In this lab you will study the motion of a simple pendulum. A simple pendulum is a pendulum that has a small amplitude of swing, i.e.,

More information

226 Chapter 15: OSCILLATIONS

226 Chapter 15: OSCILLATIONS Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion

More information

Physics 101 Exam 1 NAME 2/7

Physics 101 Exam 1 NAME 2/7 Physics 101 Exam 1 NAME 2/7 1 In the situation below, a person pulls a string attached to block A, which is in turn attached to another, heavier block B via a second string (a) Which block has the larger

More information

UNIT 14: HARMONIC MOTION

UNIT 14: HARMONIC MOTION Name St.No. - Date(YY/MM/DD) / / Section UNIT 14: HARMONIC MOTION Approximate Time three 100-minute sessions Back and Forth and Back and Forth... Cameo OBJECTIVES 1. To learn directly about some of the

More information

Chapter 24 Physical Pendulum

Chapter 24 Physical Pendulum Chapter 4 Physical Pendulum 4.1 Introduction... 1 4.1.1 Simple Pendulum: Torque Approach... 1 4. Physical Pendulum... 4.3 Worked Examples... 4 Example 4.1 Oscillating Rod... 4 Example 4.3 Torsional Oscillator...

More information

8 SIMPLE HARMONIC MOTION

8 SIMPLE HARMONIC MOTION 8 SIMPLE HARMONIC MOTION Chapter 8 Simple Harmonic Motion Objectives After studying this chapter you should be able to model oscillations; be able to derive laws to describe oscillations; be able to use

More information

Recitation 2 Chapters 12 and 13

Recitation 2 Chapters 12 and 13 Recitation 2 Chapters 12 and 13 Problem 12.20. 65.0 kg bungee jumper steps off a bridge with a light bungee cord tied to her and the bridge (Figure P12.20. The unstretched length of the cord is 11.0 m.

More information

HOOKE S LAW AND SIMPLE HARMONIC MOTION

HOOKE S LAW AND SIMPLE HARMONIC MOTION HOOKE S LAW AND SIMPLE HARMONIC MOTION Alexander Sapozhnikov, Brooklyn College CUNY, New York, alexs@brooklyn.cuny.edu Objectives Study Hooke s Law and measure the spring constant. Study Simple Harmonic

More information

Physics 1022: Chapter 14 Waves

Physics 1022: Chapter 14 Waves Phys 10: Introduction, Pg 1 Physics 10: Chapter 14 Waves Anatomy of a wave Simple harmonic motion Energy and simple harmonic motion Phys 10: Introduction, Pg Page 1 1 Waves New Topic Phys 10: Introduction,

More information

PHYS-2020: General Physics II Course Lecture Notes Section VII

PHYS-2020: General Physics II Course Lecture Notes Section VII PHYS-2020: General Physics II Course Lecture Notes Section VII Dr. Donald G. Luttermoser East Tennessee State University Edition 4.0 Abstract These class notes are designed for use of the instructor and

More information

turn-table in terms of SHM and UCM: be plotted as a sine wave. n Think about spinning a ball on a string or a ball on a

turn-table in terms of SHM and UCM: be plotted as a sine wave. n Think about spinning a ball on a string or a ball on a RECALL: Angular Displacement & Angular Velocity Think about spinning a ball on a string or a ball on a turn-table in terms of SHM and UCM: If you look at the ball from the side, its motion could be plotted

More information

7. Kinetic Energy and Work

7. Kinetic Energy and Work Kinetic Energy: 7. Kinetic Energy and Work The kinetic energy of a moving object: k = 1 2 mv 2 Kinetic energy is proportional to the square of the velocity. If the velocity of an object doubles, the kinetic

More information

Computer Experiment. Simple Harmonic Motion. Kinematics and Dynamics of Simple Harmonic Motion. Evaluation copy

Computer Experiment. Simple Harmonic Motion. Kinematics and Dynamics of Simple Harmonic Motion. Evaluation copy INTRODUCTION Simple Harmonic Motion Kinematics and Dynamics of Simple Harmonic Motion Computer Experiment 16 When you suspend an object from a spring, the spring will stretch. If you pull on the object,

More information

Experiment 5: Newton s Second Law

Experiment 5: Newton s Second Law Name Section Date Introduction Experiment : Newton s Second Law In this laboratory experiment you will consider Newton s second law of motion, which states that an object will accelerate if an unbalanced

More information

Graphical Presentation of Data

Graphical Presentation of Data Graphical Presentation of Data Guidelines for Making Graphs Titles should tell the reader exactly what is graphed Remove stray lines, legends, points, and any other unintended additions by the computer

More information

Chapter Test. Teacher Notes and Answers Forces and the Laws of Motion. Assessment

Chapter Test. Teacher Notes and Answers Forces and the Laws of Motion. Assessment Assessment Chapter Test A Teacher Notes and Answers Forces and the Laws of Motion CHAPTER TEST A (GENERAL) 1. c 2. d 3. d 4. c 5. c 6. c 7. c 8. b 9. d 10. d 11. c 12. a 13. d 14. d 15. b 16. d 17. c 18.

More information

Homework #7 Solutions

Homework #7 Solutions MAT 0 Spring 201 Problems Homework #7 Solutions Section.: 4, 18, 22, 24, 4, 40 Section.4: 4, abc, 16, 18, 22. Omit the graphing part on problems 16 and 18...4. Find the general solution to the differential

More information

1: (ta initials) 2: first name (print) last name (print) brock id (ab13cd) (lab date)

1: (ta initials) 2: first name (print) last name (print) brock id (ab13cd) (lab date) 1: (ta initials) 2: first name (print) last name (print) brock id (ab13cd) (lab date) Experiment 5 Harmonic motion In this Experiment you will learn that Hooke s Law F = kx can be used to model the interaction

More information

Experiment 9. The Pendulum

Experiment 9. The Pendulum Experiment 9 The Pendulum 9.1 Objectives Investigate the functional dependence of the period (τ) 1 of a pendulum on its length (L), the mass of its bob (m), and the starting angle (θ 0 ). Use a pendulum

More information

Work. Work = Force distance (the force must be parallel to movement) OR Work = (Force)(cos θ)(distance)

Work. Work = Force distance (the force must be parallel to movement) OR Work = (Force)(cos θ)(distance) Work Work = Force distance (the force must be parallel to movement) OR Work = (Force)(cos θ)(distance) When you are determining the force parallel to the movement you can do this manually and keep track

More information

Physics 41 HW Set 1 Chapter 15

Physics 41 HW Set 1 Chapter 15 Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,

More information

Mechanical Vibrations

Mechanical Vibrations Mechanical Vibrations A mass m is suspended at the end of a spring, its weight stretches the spring by a length L to reach a static state (the equilibrium position of the system). Let u(t) denote the displacement,

More information

Center of Mass/Momentum

Center of Mass/Momentum Center of Mass/Momentum 1. 2. An L-shaped piece, represented by the shaded area on the figure, is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the L-shaped

More information

Energy transformations

Energy transformations Energy transformations Objectives Describe examples of energy transformations. Demonstrate and apply the law of conservation of energy to a system involving a vertical spring and mass. Design and implement

More information

Centripetal Force. 1. Introduction

Centripetal Force. 1. Introduction 1. Introduction Centripetal Force When an object travels in a circle, even at constant speed, it is undergoing acceleration. In this case the acceleration acts not to increase or decrease the magnitude

More information

A) F = k x B) F = k C) F = x k D) F = x + k E) None of these.

A) F = k x B) F = k C) F = x k D) F = x + k E) None of these. CT16-1 Which of the following is necessary to make an object oscillate? i. a stable equilibrium ii. little or no friction iii. a disturbance A: i only B: ii only C: iii only D: i and iii E: All three Answer:

More information

Applications of Second-Order Differential Equations

Applications of Second-Order Differential Equations Applications of Second-Order Differential Equations Second-order linear differential equations have a variety of applications in science and engineering. In this section we explore two of them: the vibration

More information

The moment of inertia of a rod rotating about its centre is given by:

The moment of inertia of a rod rotating about its centre is given by: Pendulum Physics 161 Introduction This experiment is designed to study the motion of a pendulum consisting of a rod and a mass attached to it. The period of the pendulum will be measured using three different

More information

Physics 211 Week 12. Simple Harmonic Motion: Equation of Motion

Physics 211 Week 12. Simple Harmonic Motion: Equation of Motion Physics 11 Week 1 Simple Harmonic Motion: Equation of Motion A mass M rests on a frictionless table and is connected to a spring of spring constant k. The other end of the spring is fixed to a vertical

More information

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

More information

Mh1: Simple Harmonic Motion. Chapter 15. Motion of a Spring-Mass System. Periodic Motion. Oscillatory Motion

Mh1: Simple Harmonic Motion. Chapter 15. Motion of a Spring-Mass System. Periodic Motion. Oscillatory Motion Mh1: Siple Haronic Motion Chapter 15 Siple block and spring Oscillatory Motion Exaple: the tides, a swing Professor Michael Burton School of Physics, UNSW Periodic Motion! Periodic otion is otion of an

More information

16 OSCILLATORY MOTION AND WAVES

16 OSCILLATORY MOTION AND WAVES CHAPTER 16 OSCILLATORY MOTION AND WAVES 549 16 OSCILLATORY MOTION AND WAVES Figure 16.1 There are at least four types of waves in this picture only the water waves are evident. There are also sound waves,

More information

Response to Harmonic Excitation

Response to Harmonic Excitation Response to Harmonic Excitation Part 1 : Undamped Systems Harmonic excitation refers to a sinusoidal external force of a certain frequency applied to a system. The response of a system to harmonic excitation

More information

Oscillations. Vern Lindberg. June 10, 2010

Oscillations. Vern Lindberg. June 10, 2010 Oscillations Vern Lindberg June 10, 2010 You have discussed oscillations in Vibs and Waves: we will therefore touch lightly on Chapter 3, mainly trying to refresh your memory and extend the concepts. 1

More information

SIMPLE HARMONIC MOTION

SIMPLE HARMONIC MOTION PERIODIC MOTION SIMPLE HARMONIC MOTION If a particle moves such that it repeats its path regularly after equal intervals of time, its motion is said to be periodic. The interval of time required to complete

More information

Solutions 2.4-Page 140

Solutions 2.4-Page 140 Solutions.4-Page 4 Problem 3 A mass of 3 kg is attached to the end of a spring that is stretched cm by a force of 5N. It is set in motion with initial position = and initial velocity v = m/s. Find the

More information

Physics 1120: Simple Harmonic Motion Solutions

Physics 1120: Simple Harmonic Motion Solutions Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Physics 1120: Simple Harmonic Motion Solutions 1. A 1.75 kg particle moves as function of time as follows: x = 4cos(1.33t+π/5) where distance is measured

More information

BROCK UNIVERSITY. PHYS 1P21/1P91 Solutions to Mid-term test 26 October 2013 Instructor: S. D Agostino

BROCK UNIVERSITY. PHYS 1P21/1P91 Solutions to Mid-term test 26 October 2013 Instructor: S. D Agostino BROCK UNIVERSITY PHYS 1P21/1P91 Solutions to Mid-term test 26 October 2013 Instructor: S. D Agostino 1. [10 marks] Clearly indicate whether each statement is TRUE or FALSE. Then provide a clear, brief,

More information

Wave Motion (Chapter 15)

Wave Motion (Chapter 15) Wave Motion (Chapter 15) Waves are moving oscillations. They transport energy and momentum through space without transporting matter. In mechanical waves this happens via a disturbance in a medium. Transverse

More information

Chapter 07: Kinetic Energy and Work

Chapter 07: Kinetic Energy and Work Chapter 07: Kinetic Energy and Work Conservation of Energy is one of Nature s fundamental laws that is not violated. Energy can take on different forms in a given system. This chapter we will discuss work

More information

ELASTIC FORCES and HOOKE S LAW

ELASTIC FORCES and HOOKE S LAW PHYS-101 LAB-03 ELASTIC FORCES and HOOKE S LAW 1. Objective The objective of this lab is to show that the response of a spring when an external agent changes its equilibrium length by x can be described

More information

11/27/2014 Partner: Diem Tran. Bungee Lab I: Exploring the Relationship Between Bungee Cord Length and Spring Force Constant

11/27/2014 Partner: Diem Tran. Bungee Lab I: Exploring the Relationship Between Bungee Cord Length and Spring Force Constant Bungee Lab I: Exploring the Relationship Between Bungee Cord Length and Spring Force Constant Introduction: This lab relies on an understanding of the motion of a spring and spring constant to facilitate

More information

Lecture L19 - Vibration, Normal Modes, Natural Frequencies, Instability

Lecture L19 - Vibration, Normal Modes, Natural Frequencies, Instability S. Widnall 16.07 Dynamics Fall 2009 Version 1.0 Lecture L19 - Vibration, Normal Modes, Natural Frequencies, Instability Vibration, Instability An important class of problems in dynamics concerns the free

More information

Waves and Sound. An Introduction to Waves and Wave Properties Wednesday, November 19, 2008

Waves and Sound. An Introduction to Waves and Wave Properties Wednesday, November 19, 2008 Waves and Sound An Introduction to Waves and Wave Properties Wednesday, November 19, 2008 Mechanical Wave A mechanical wave is a disturbance which propagates through a medium with little or no net displacement

More information

FRICTION, WORK, AND THE INCLINED PLANE

FRICTION, WORK, AND THE INCLINED PLANE FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle

More information

SOLUTIONS TO PROBLEM SET 4

SOLUTIONS TO PROBLEM SET 4 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01X Fall Term 2002 SOLUTIONS TO PROBLEM SET 4 1 Young & Friedman 5 26 A box of bananas weighing 40.0 N rests on a horizontal surface.

More information

SIMPLE HARMONIC MOTION Ken Cheney

SIMPLE HARMONIC MOTION Ken Cheney SIMPLE HARMONIC MOTION Ken Cheney INTRODUCTION GENERAL Probably no tools that you will learn in Physics are more widely used than those that deal with simple harmonic motion. Here we will be investigating

More information