# SIMPLE HARMONIC MOTION

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 can be appreciated by listing a few examples that include pendulum motion, the oscillating circuit used to tune a radio receiver, and the bobbing motion of a car with worn shock absorbers. Less common, but perhaps more interesting to the physicist are the interatomic vibrations of molecules, the motion of gas molecules propagating a sound wave, and the time behavior of electric and magnetic fields (including light) traveling through space. Probably the simplest form of simple harmonic motion is the oscillation of a mass suspended from a vertical spring. It is this form we will be studying in this lab. We will determine the elastic spring constant K of a spring first and then study small vertical oscillations of a mass suspended from the spring. THEORY How can so many diverse systems exhibit essentially the same kind of motion? The answer lies in the fact that each of these systems obeys the same fundamental mathematical equation. Let's quickly review how this equation comes about in the case of a mass suspended from a spring. The springs you will be using obey Hooke's Law, F s = - K (x - x o ) (1) Here, x o is the equilibrium position of the spring and the minus sign indicates that the force exerted by the spring is in the opposite direction to the displacement, (x - x o ), of the mass. This equation can be taken as the defining relation for the spring constant K. The textbook shows how to apply Hooke's Law along with Newton's Second Law to the motion of a mass M on a frictionless surface and connected to a horizontal spring of force constant K. The analysis results in the equation, d 2 s/dt 2 + (K / m) s = 0 (2) where s = x - x o. This is the differential equation simple harmonic motion. Every physical system that exhibits simple harmonic motion obeys an equation of this form. The most general solution to this equation can be written as s(t) = A cos(ωt + φ) (3) where the constants A and φ are determined from the initial position and velocity of the mass M. The constant ω is the angular frequency and is given by ω = (K / m) 1/2 (4) The angular frequency provides the time period of the motion, SIMPLE HARMONIC MOTION V-1

2 T = 2 π (m / K) 1/2 (5) In our experiment we will be working with a vertical spring-mass system. The analysis of this system yields the exact same differential equation as in the horizontal case, however, now the equilibrium position is changed by the amount the spring stretches under the weight W = M g. As an exercise you should make sure you can carry out all the details of this analysis. Since the vertical spring-mass system obeys the same equation of motion as the horizontal one, the dynamics of the two systems are identical. In particular, the time period of motion is again given by Equation 5. This period relation suggests a way to experimentally determine the spring constant K. Squaring both sides of Equation 3 gives T 2 = 4 π 2 (M / K) (6) By suspending various masses from the spring and measuring the corresponding periods we can construct a graph of T 2 vs. M. Equation (6) predicts that this relationship is linear with a slope of 4 π 2 (1 / K). Having constructed this graph we can determine the line of best fit through the data points (M i, T i 2 ) and measure the slope. The spring constant is then just K = 4 π 2 (1 / SLOPE) (7) Correction for the finite mass of the spring We must also consider the mass of the spring itself. The textbook derivation of the period relation, Equation 3, is based on a spring of negligible mass. In reality, springs have finite mass and therefore possess kinetic energy while in motion. We must thus consider the finite mass of the spring in the dynamics of our spring-mass system. Let m s be the mass of the spring. The inclusion of m s in the analysis results in a corrected mass which appears in the equations above. The true mass is the suspended mass, M, plus some fraction of the mass of the spring. That is, in all the equations above, we let M true = M + R m s (8) where R is an, as yet, undetermined fraction between 0 and 1. The true period is found by using M true in Equation 3 for the time period. The result is the corrected period given as T true = 2 π (M true / K) 1/2 (9) What is R? A moment's thought should reveal that R = 1 is too large, for it implies that the entire mass of the spring contributes to the oscillations. Not all of the mass of the spring oscillates with the same amplitude. We can determine R experimentally however. EXPERIMENTAL PROCEDURE 1. Measure the mass, M', which is the mass of the weight holder plus a 200 g mass. (Note that) Suspend one of the springs and the mass M' vertically from the support. Allow it to come to rest and measure the distance from the floor to the bottom of the weight holder. SIMPLE HARMONIC MOTION V-2

4 3. Using a straight edge or a ruler, sketch the best straight line fit to these data points. Determine the slope of this straight line. The slope is in units of g cm -1. (Fit it on the computer.) 4. The spring constant K = (slope) (acceleration due to gravity). Remember to convert the slope units to kg m -1. Assume acceleration due to gravity = 9.8 m sec Using data from Table 2, plot T 2 vs. Mass suspended from the spring on another graph paper. Origin of co-ordinates must be (0,0). 6. The slope of T 2 (vertical axis) vs. mass suspended (horizontal axis) is in s 2 g -1. This value can be converted to s 2 kg -1 and the spring constant can be determined using the equation for the elastic spring constant: K = 4 π 2 (1 / SLOPE) (7) where the slope is given in s 2 kg Determine the intercept on the negative horizontal axis. This gives the contribution from the spring to the oscillating mass. Compare this to the mass (m s ) of the spring. SIMPLE HARMONIC MOTION V-4

5 NAME Sec/Group Date DATA TABLE 1 ELASTIC CONSTANT, K, OF THE SPRING # Suspended Mass ( in g ) Distance Extension Mass (in g ) (added to M') (in cm ) ( in cm ) 1 M' = 0 L 0 = L 0 - L 0 = 0 2 M' + = L 1 = L 0 - L 1 = 3 M' + = L 2 = L 0 - L 2 = 4 M' + = L 3 = L 0 - L 3 = 5 M' + = L 4 = L 0 - L 4 = 6 M' + = L 5 = L 0 - L 5 = Mass of spring = g Acceleration due to gravity g = 9.8 m s -2 Slope of mass added (y-axis ) vs. extension ( x-axis ) = g cm -1 = kg m -1 Elastic spring constant K = ( slope in kg m -1 ) ( acceleration due to gravity in m s -2 ) = N m -1 SIMPLE HARMONIC MOTION V-5

6 TABLE 2 OSCILLATIONS OF MASS FROM THE SPRING # Mass Time for 10 oscillations Period M (g) T 1 (s) T 2 (s) T 3 (s) T (s) T 2 (s 2 ) 1. M" = 2. M" + = 3. M"+ = 4. M"+ = 5. M"+ = Slope of T 2 (vertical axis) vs. mass suspended (horizontal axis) = s 2 g -1 = s 2 kg -1 Elastic spring constant K = 4 π 2 / (slope in s 2 kg -1 ) = N m -1 Intercept on the negative x-axis Ratio of intercept to mass of spring, R = g = g SIMPLE HARMONIC MOTION V-6

### 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

### 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

### 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

### 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

### p = F net t (2) But, what is the net force acting on the object? Here s a little help in identifying the net force on an object:

Harmonic Oscillator Objective: Describe the position as a function of time of a harmonic oscillator. Apply the momentum principle to a harmonic oscillator. Sketch (and interpret) a graph of position as

### 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

### 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

### 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

### 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

### 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

### 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

### HOOKE'S LAW AND A SIMPLE SPRING DONALD C. PECKHAM PHYSICS 307 FALL 1983 ABSTRACT

HOOKE'S LAW AND A SIMPLE SPRING DONALD C. PECKHAM PHYSICS 307 FALL 983 (Digitized and Revised, Fall 005) ABSTRACT The spring constant of a screen-door spring was determined both statically, by measuring

### 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

### 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

### 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

### 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,

### 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

### STANDING WAVES. Objective: To verify the relationship between wave velocity, wavelength, and frequency of a transverse wave.

STANDING WAVES Objective: To verify the relationship between wave velocity, wavelength, and frequency of a transverse wave. Apparatus: Magnetic oscillator, string, mass hanger and assorted masses, pulley,

### 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

### 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

### PHYS 130 Laboratory Experiment 11 Hooke s Law & Simple Harmonic Motion

PHYS 130 Laboratory Experiment 11 Hooke s Law & Simple Harmonic Motion NAME: DATE: SECTION: PARTNERS: OBJECTIVES 1. Verify Hooke s Law and use it to measure the force constant of a spring. 2. Investigate

### 2. The graph shows how the displacement varies with time for an object undergoing simple harmonic motion.

Practice Test: 29 marks (37 minutes) Additional Problem: 31 marks (45 minutes) 1. A transverse wave travels from left to right. The diagram on the right shows how, at a particular instant of time, the

### 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

### 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

### 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

### THE SPRING CONSTANT. Apparatus: A spiral spring, a set of weights, a weight hanger, a balance, a stop watch, and a twometer

THE SPRING CONSTANT Objective: To determine the spring constant of a spiral spring by Hooe s law and by its period of oscillatory motion in response to a weight. Apparatus: A spiral spring, a set of weights,

### 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

### 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

### 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

### 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

### Sample Questions for the AP Physics 1 Exam

Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each

### 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

### 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

### Materials Design: Vibration Isolation and Damping, the Basics

Materials Design: Vibration Isolation and Damping, the Basics Vibration management should always be considered in any engineering design. Applications that have effectively incorporated vibration management

### 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

### 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

### 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.

### 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

### 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

### 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

### A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion

A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion Objective In the experiment you will determine the cart acceleration, a, and the friction force, f, experimentally for

### State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

### 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

### 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

### 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

### 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

### 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

### Simple Harmonic Motion Experiment. 1 f

Simple Harmonic Motion Experiment In this experiment, a motion sensor is used to measure the position of an oscillating mass as a function of time. The frequency of oscillations will be obtained by measuring

### Experiment P19: Simple Harmonic Motion - Mass on a Spring (Force Sensor, Motion Sensor)

PASCO scientific Physics Lab Manual: P19-1 Science Workshop S. H. M. Mass on a Spring Experiment P19: Simple Harmonic Motion - Mass on a Spring (Force Sensor, Motion Sensor) Concept Time SW Interface Macintosh

### Force. Net Force Mass. Acceleration = Section 1: Weight. Equipment Needed Qty Equipment Needed Qty Force Sensor 1 Mass and Hanger Set 1 Balance 1

Department of Physics and Geology Background orce Physical Science 1421 A force is a vector quantity capable of producing motion or a change in motion. In the SI unit system, the unit of force is the Newton

### PC1221 Fundamentals of Physics I Inertia Wheel

PC1221 Fundamentals of Physics I Inertia Wheel 1 Purpose Determination of the angular acceleration of the inertial wheel as a function of the applied torque Determination of the moment of inertia I of

### 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

### 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

### 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................

### ANALYTICAL METHODS FOR ENGINEERS

UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME - TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations

### 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

### 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

### 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

### Determination of g using a spring

INTRODUCTION UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1 Laboratory: Introduction Experiment Determination of g using a spring This experiment is designed to get you confident in using the quantitative

### 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

### Calculate the centripetal acceleration of the boot just before impact

(ii) alculate the centripetal acceleration of the boot just before impact....... (iii) iscuss briefly the radial force on the knee joint before impact and during the impact................. (4) (Total

### Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

### 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

### State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 28] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

### General Physics Lab: Atwood s Machine

General Physics Lab: Atwood s Machine Introduction One may study Newton s second law using a device known as Atwood s machine, shown below. It consists of a pulley and two hanging masses. The difference

### 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

### SAMPLE PAPER 1 XI PHYSICS

SAMPLE PAPER 1 o A n XI PHYSICS Time: Three Hours Maximum Marks: 70 General Instructions (a) All questions are compulsory. (b) There are 30 questions in total. Questions 1 to 8 carry one mark each, questions

### 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

### = 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

### 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

### 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

### AP Physics Energy and Springs

AP Physics Energy and Springs Another major potential energy area that AP Physics is enamored of is the spring (the wire coil deals, not the ones that produce water for thirsty humanoids). Now you ve seen

### Standing Waves on a String

1 of 6 Standing Waves on a String Summer 2004 Standing Waves on a String If a string is tied between two fixed supports, pulled tightly and sharply plucked at one end, a pulse will travel from one end

### 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,

### 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

### AP1 Gravity. at an altitude equal to twice the radius (R) of the planet. What is the satellite s speed assuming a perfectly circular orbit?

1. A satellite of mass m S orbits a planet of mass m P at an altitude equal to twice the radius (R) of the planet. What is the satellite s speed assuming a perfectly circular orbit? (A) v = Gm P R (C)

### 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

### Physics 305 Homework Solutions Page 1 Waves and Wavefunctions

Physics 305 Homework Solutions Page 1 1) The figure below represents the profile (t = 0 s) of a transverse wave on a string traveling in the positive x direction at a speed of 100 cm/s. (The values for

### Equilibrium. To determine the mass of unknown objects by utilizing the known force requirements of an equilibrium

Equilibrium Object To determine the mass of unknown objects by utilizing the known force requirements of an equilibrium situation. 2 Apparatus orce table, masses, mass pans, metal loop, pulleys, strings,

### Chapter 6 Work and Energy

Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system

### Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath

Physics 271 FINAL EXAM-SOLUTIONS Friday Dec 23, 2005 Prof. Amitabh Lath 1. The exam will last from 8:00 am to 11:00 am. Use a # 2 pencil to make entries on the answer sheet. Enter the following id information

### Experiment Type: Open-Ended

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

### Physics 53. Wave Motion 1

Physics 53 Wave Motion 1 It's just a job. Grass grows, waves pound the sand, I beat people up. Muhammad Ali Overview To transport energy, momentum or angular momentum from one place to another, one can

### Rotational Mechanics - 1

Rotational Mechanics - 1 The Radian The radian is a unit of angular measure. The radian can be defined as the arc length s along a circle divided by the radius r. s r Comparing degrees and radians 360

### Waves I: Generalities, Superposition & Standing Waves

Chapter 5 Waves I: Generalities, Superposition & Standing Waves 5.1 The Important Stuff 5.1.1 Wave Motion Wave motion occurs when the mass elements of a medium such as a taut string or the surface of a

### 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...

### Mid-Chapter Quiz: Lessons 4-1 through 4-4

Find the exact values of the six trigonometric functions of θ. Find the value of x. Round to the nearest tenth if necessary. 1. The length of the side opposite is 24, the length of the side adjacent to

### 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)

### SHM Simple Harmonic Motion revised June 16, 2012

SHM Simple Harmonic Motion revised June 16, 01 Learning Objectives: During this lab, you will 1. communicate scientific results in writing.. estimate the uncertainty in a quantity that is calculated from

### Physics 271, Sections H1 & H2 Thursday, Nov 20, 2014

Physics 271, Sections H1 & H2 Thursday, Nov 20, 2014 Problems #11 Oscillations 1) Consider a mass spring system, with mass M and spring constant k. We put a mass m on top of the mass M. The coefficient

### General Physics I Can Statements

General Physics I Can Statements Motion (Kinematics) 1. I can describe motion in terms of position (x), displacement (Δx), distance (d), speed (s), velocity (v), acceleration (a), and time (t). A. I can

### HOMEWORK FOR UNIT 5-1: FORCE AND MOTION

Name Date Partners HOMEWORK FOR UNIT 51: FORCE AND MOTION 1. You are given ten identical springs. Describe how you would develop a scale of force (ie., a means of producing repeatable forces of a variety

### Tennessee State University

Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.

### Experiment: Static and Kinetic Friction

PHY 201: General Physics I Lab page 1 of 6 OBJECTIVES Experiment: Static and Kinetic Friction Use a Force Sensor to measure the force of static friction. Determine the relationship between force of static

### S15--AP Phys Q3 SHO-Sound PRACTICE

Name: Class: Date: ID: A S5--AP Phys Q3 SHO-Sound PRACTICE Multiple Choice Identify the choice that best completes the statement or answers the question.. If you are on a train, how will the pitch of the

### 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,

### The Pendulum. Experiment #1 NOTE:

The Pendulum Experiment #1 NOTE: For submitting the report on this laboratory session you will need a report booklet of the type that can be purchased at the McGill Bookstore. The material of the course

### 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