VIBRATION DUE TO ROTATION UNBALANCE


 Elvin Flowers
 2 years ago
 Views:
Transcription
1 Fall 08 Prepared by: Keivan Anbarani Abstract In this experiment four eccentric masses are used in conjunction with four springs and one damper to simulate the vibration. Masses are aligned in different orders to simulate in phase and out phase situation. Acceleration, frequency and phase shift of the system is measure, which then are used to do calculations and generating graphs to describe the simple harmonic motion. For in phase situation natural frequency is measured to be 9.16 Hz and calculated to be 9.6 Hz. This is a fairly good result since in real life nothing is perfect and it is not possible to generate theoretical results. As expected the calculated natural frequency is slightly larger due to the fact that damping is assumed to be zero using theoretical calculation, where the system really is slightly damped. For out phase situation natural frequency happens at frequency of Hz and also at 6.13 Hz, however at Hz the amplitude is much larger.
2 Table of Contents 1.0 INTRODUCTION METHODS RESULTS...2 Sample Phase Shift Calculation...2 Pre filtered and Post filtered Signals...3 In Phase Results...3 Experimental versus Theoretical comparison... 5 Damping ratio calculation:... 6 Out of Phase...7 Damping ratio calculation: DISCUSSION AND CONCLUSION LEARNING OUTCOMES...10
3 1.0 INTRODUCTION Vibration due to rotating eccentric masses is a common phenomenal that one sees in everyday life such as vibration of automobile engine or the washing machine. This phenomenal is really important because if not dealt with promptly one could have catastrophic failures due to the fatigue caused by the vibration. As observed in this lab at natural frequency vibration force could get really big which could lead into an unstable system and causing failure. 2.0 METHODS As shown in figure 1, this experiment consists of: Engine Model: The box that contains the shaft and essentric masses Optical Encoder: used to generate an optical pulse per rotation of essentric mass Speed Control: used to control the speed of rotation Accelerometer: a piezoelectric element that produces an electric charge when subject to a load, it is used to measure the vertical acceleration. There is one rectangular box which could model Figure 1  Experiment Apparatus a cars engine. The front and back of the system contains two rotating shaft which have two essentric masses attached to them. In total there are four essentric masses that rotate. For in phase all the masses are pointing in the same direction to start with, for our phase masses point opposite of the masses on the other side. Figure 2 is the front view of the experiment which is really simular to the back view. Figure 3 shows the arrangments of the 4 springs and the damper from the side. The values that are measured with hand in this lab are the radious of the eccentric mass, the distance of the masses from the Figure 2  Front view of the system center, which is where the damper is located. The values that are measured with computer are frequency, acceleration and the phase shift. Figure 3  Side view of the system Page 1 VIBRATION DUE TO ROTATION UNBALANCE
4 3.0 RESULTS This section illustrates how Matlab measures frequency, amplitude and phase shift to determine how the system behaves for given frequencies. Graphs will also be included in this section to help understand these calculations. Sample Phase Shift Calculation In order to determine the phase shift, snapshot of the figure 4 is taken and the following formula is used. φ = 360 τω 360, where τ is the difference 2π between the leading edge of the pulse signal and the upward zero crossing of the sign wave which the system is oscillating. The sample phase shift calculation below is done at 19.65Hz. φ = 360 ( ) (19.65) 2π 360 = Figure 4  Graph used to measure phase shift The sample phase shift is calculated to be , however Matlab calculates the value to be The calculated error in terms of time is only seconds, which is acceptable since the data was taken from the graph. t = φ 360 f t = ( ) 360 (19.65) =.021seconds Page 2
5 Pre filtered and Post filtered Signals There are so many noises involved in this experiment. Therefore, a filter is being used in order to get a clear signal. A band pass filtration system is used for this specific experiment. The figures below is taken before and after filtration is used so that it is clear why filtration is needed. Figure 5  Pre filtered signal Figure 6 Post filtered signal In Phase Results An experiment is conducted to determine the system s behavior for varies of frequencies. The measured values are Acceleration, Frequency and Phase shift. However acceleration is measured in Volts and later converted to m/s 2 using the conversion factor of 9.81 m/s 2 = 99 mv. Also rotation speed is measured in rotation per minute and one rotation is equivalent to 2π. These values are then used in the following formula to calculate systems excitation vertical displacement. x = x, where x is the vertical displacement, x is the vertical acceleration of the system and ω is the 2 ω rotation speed. The system showed maximum displacement at 9.16 Hz. Resonance frequency is a term used to define the tendency of a system to oscillate at larger amplitude at some frequencies than at others, therefore in this experiment the experimental resonance frequency is 9.16 Hz. Theoretical value for un damped resonance frequency ω n, is calculated using the following formula ω n = k M where k is the spring constant and M is mass of the whole system. ω n = Page N / m kg 2πrad = 9.6s 1
6 Based on our experimental graph the maximum displacement is measured to be at 0.13 cm, however the theoretical value for the maximum displacement is calculated to be 0.14 cm. There is a slight difference and that is because there are external forces that was not taken into account when calculating the theoretical value such as friction between the bearings, air friction and damping of the system. Figure 7 Experimental displacement versus rotation speed graph Figure 8  Experimental Phase shift versus rotation speed graph Page 4
7 Experimental versus Theoretical comparison In the shaky table the system s motion can be described as a second order differential equation. Which is: M d 2 x dt 2 + C dx dt + kx = 4meω2 sin(ωt) the solution for this second order differential equation is x(t) = e ξω nt [Acos(ω d t) + Bsin(ω d t) + Y sin(ωt Φ) where the red part of the equation is the homogeneous solution and the blue part is particular solution which is what we are interested in this lab. Frequency response function is a dimensionless function which is the ratio of the output to input expressed as a function of excitation frequency. x u = r 2 (1 r 2 ) 2 + (2ζr), where r = ω and u = 4me 2 ω n M e is the essentric radious, m is the essentric mass and M is the mass of the system. Above equation was used to plot the theoretical displacement versus rotation speed graph. Figure 9 Displacement comparison graph As showen in figure 9 the maximum theoritical displacement is 0.14 cm, but the experimental value is 0.13 cm. Page 5
8 Figure 11 Frequency Response curves equation illustration Figure 10 Frequency response curve Figure 11 reproduces the curve in figure 6 for the damping value. Damping ratio calculation: In order to estimate the damping coefficient, the decrement in amplitude is estimated by taking two consecutive amplitudes and measuring their difference. We considered a few different cycles to get the most accurate value. The following equation and graph is used to determine the damping coefficient of the system. δ = ln( A i A i+r ) 1 r, ζ δ 2π where r is the number of cycles and A i and A i+r. A i r A i+r δ ζ Taking the average = Figure 12 In phase damping The damping coefficient ζ turns out to be Page 6
9 Out of Phase The same methods as in phase section is used to calculate and plot the following graphs. Figure 12  Phase shift Figure 13 Frequency response Page 7
10 Damping ratio calculation: In order to estimate the damping coefficient, the decrement in amplitude is estimated by taking two consecutive amplitudes and measuring their difference. We considered a few different cycles to get the most accurate value. The following equation and graph is used to determine the damping coefficient of the system. δ = ln( A i A i+r ) 1 r, ζ δ 2π where r is the number of cycles and A i and A i+r. A i r A i+r δ ζ The damping coefficient ζ turns out to be Figure 14 Out phase damping Page 8
11 4.0 DISCUSSION AND CONCLUSION Quantity Formula In phase Out of phase Resonant frequency ω n = 4k m 9.6 Hz Hz Maximum Acceleration Level 98mV cm 9.81m / s 2 s cm s 2!" #$% Maximum Displacement!#$% Modal stiffness, k x = x ω cm 1.16 cm F k = 2ζX max N m N m Modal Mass, m m = k ω 2 n 24 kg 2.2 kg Modal damping, c c = F kg/s 9.7 kg/s ω n X max Resonant frequency is the point that the system has maximum oscillation and in out of phase case we have two natural frequencies, one around 7 Hz and other around 11 Hz. The damping ratio at 7 Hz is much smaller because r is equal to 1. The source of error in our theoretical versus experimental values includes friction, air drag and the damper since we assume zero damping for the theoretical calculations. Channel two didn't show a clear harmonic acceleration response because there are other external forces that could affect the harmonic motion such as, air friction, internal friction for the motor and the mass of the spring. There is a big phase shift close to the resonance. Right before resonance the phase shift was 209 and at resonance it jumps to 311 We excited the system as close to resonance as possible so we can observe the maximum amplitude respond. Page 9
12 5.0 LEARNING OUTCOMES In this experiment I learned the importance of excitation frequency on vibration response and how one can use computer measurements and graphs to calculate important values such as damping coefficient. My team being the first group to do this experiment had extremely hard time preparing this report due to lack of understanding of the equations and concepts of the experiment. However thankfully with the help of the TA and Dr. Srikanth we were able to understand everything and finish the lab with excellent results. Page 10
A C O U S T I C S of W O O D Lecture 3
Jan Tippner, Dep. of Wood Science, FFWT MU Brno jan. tippner@mendelu. cz Content of lecture 3: 1. Damping 2. Internal friction in the wood Content of lecture 3: 1. Damping 2. Internal friction in the wood
More informationDesign for Vibration Suppression
Design for Vibration Suppression Outlines: 1. Vibration Design Process. Design of Vibration Isolation Moving base Fixed base 3. Design of Vibration Absorbers Vibration Design Process Actual system Modeling
More informationName: 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 information1.10 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 informationResonance. The purpose of this experiment is to observe and evaluate the phenomenon of resonance.
Resonance Objective: The purpose of this experiment is to observe and evaluate the phenomenon of resonance. Background: Resonance is a wave effect that occurs when an object has a natural frequency that
More informationHooke 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 informationFrom Figure 5.1, an rms displacement of 1 mm (1000 µm) would not cause wall damage at frequencies below 3.2 Hz.
51 Problems and Solutions Section 5.1 (5.1 through 5.5) 5.1 Using the nomograph of Figure 5.1, determine the frequency range of vibration for which a machine oscillation remains at a satisfactory level
More informationHooke s Law. Spring. Simple Harmonic Motion. Energy. 12/9/09 Physics 201, UWMadison 1
Hooke s Law Spring Simple Harmonic Motion Energy 12/9/09 Physics 201, UWMadison 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, UWMadison 2 We know
More informationMaterials 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
More informationSimple 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 informationAdvanced 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 informationSIMPLE 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 informationPeriodic 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 informationDynamic Response of Measurement Systems
ME231 Measurements Laboratory Spring 1999 Dynamic Response of Measurement Systems Edmundo Corona c The handout Getting Ready to Measure presented a couple of examples where the results of a static calibration
More informationSimple 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 informationExperiment 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= 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 informationResonance. The purpose of this experiment is to observe and evaluate the phenomenon of resonance.
Resonance Objective: The purpose of this experiment is to observe and evaluate the phenomenon of resonance. Background: Resonance is the tendency of a system to oscillate with greater amplitude at some
More informationp = 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
More informationPeople s Physics book 3e Ch 251
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 informationHOOKE'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 screendoor spring was determined both statically, by measuring
More informationAP1 Oscillations. 1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false?
1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The
More informationSlide 10.1. Basic system Models
Slide 10.1 Basic system Models Objectives: Devise Models from basic building blocks of mechanical, electrical, fluid and thermal systems Recognize analogies between mechanical, electrical, fluid and thermal
More informationPhysics 2101 Section 3 Apr 14th Announcements: Quiz Friday Midterm #4, April Midterm #4,
Physics 2101 Section 3 Apr 14 th Announcements: Quiz Friday Midterm #4, April 28 th Final: May 11 th7:30am Class Website: 6 pm Make up Final: May 15 th 7:30am http://www.phys.lsu.edu/classes/spring2010/phys2101
More informationSolutions 2.4Page 140
Solutions.4Page 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 informationHOOKE'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 massspring system obeys Hooke's Law and to study simple harmonic motion. THEORY
More informationCoupled Electrical Oscillators Physics 3600 Advanced Physics Lab Summer 2010 Don Heiman, Northeastern University, 5/10/10
Coupled Electrical Oscillators Physics 3600 Advanced Physics Lab Summer 00 Don Heiman, Northeastern University, 5/0/0 I. Introduction The objectives of this experiment are: () explore the properties of
More informationMAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START
Laboratory Section: Last Revised on September 21, 2016 Partners Names: Grade: EXPERIMENT 11 Velocity of Waves 0. PreLaboratory Work [2 pts] 1.) What is the longest wavelength at which a sound wave will
More informationMECHANICS IV  SIMPLE HARMONIC MOTION
MIVp.1 A. OSCILLATIONS B. SIMPLE PENDULUM C. KINEMATICS OF SIMPLE HARMONIC MOTION D. SPRINGANDMASS SYSTEM E. ENERGY OF SHM F. DAMPED HARMONIC MOTION G. FORCED VIBRATION A. OSCILLATIONS A toandfro
More informationSimple 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 information2. 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
More information2.3 Cantilever linear oscillations
.3 Cantilever linear oscillations Study of a cantilever oscillation is a rather science  intensive problem. In many cases the general solution to the cantilever equation of motion can not be obtained
More informationExperiment Type: OpenEnded
Simple Harmonic Oscillation Overview Experiment Type: OpenEnded In this experiment, students will look at three kinds of oscillators and determine whether or not they can be approximated as simple harmonic
More information8 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 informationChapter 13, example problems: x (cm) 10.0
Chapter 13, example problems: (13.04) Reading Fig. 1330 (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 informationResponse to Harmonic Excitation Part 2: Damped Systems
Response to Harmonic Excitation Part 2: Damped Systems Part 1 covered the response of a single degree of freedom system to harmonic excitation without considering the effects of damping. However, almost
More informationSimple 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 Rightangled
More information6: STANDING WAVES IN STRINGS
6: STANDING WAVES IN STRINGS 1. THE STANDING WAVE APPARATUS It is difficult to get accurate results for standing waves with the spring and stopwatch (last week s Lab 4B). In contrast, very accurate results
More informationLABORATORY 9. Simple Harmonic Motion
LABORATORY 9 Simple Harmonic Motion Purpose In this experiment we will investigate two examples of simple harmonic motion: the massspring system and the simple pendulum. For the massspring system we
More informationSIMPLE 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 informationSoil Dynamics Prof. Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology, Bombay
Soil Dynamics Prof. Deepankar Choudhury Department of Civil Engineering Indian Institute of Technology, Bombay Module  2 Vibration Theory Lecture  8 Forced Vibrations, Dynamic Magnification Factor Let
More informationHOOKE 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 informationPhysics 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 informationResonance in a piezoelectric material
Resonance in a piezoelectric material Daniel L. Tremblay Physics Department, The College of Wooster, Wooster, Ohio 44691 May 8, 2006 An AC voltage was used in conjunction with a piezoelectric material
More informationLab 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 informationChapter 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 informationTHE 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,
More informationRecitation 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 informationAP 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 information11 Vibration Analysis
11 Vibration Analysis 11.1 Introduction A spring and a mass interact with one another to form a system that resonates at their characteristic natural frequency. If energy is applied to a spring mass system,
More informationWaves 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
More informationSHM 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
More informationCHAPTER 5 THE HARMONIC OSCILLATOR
CHAPTER 5 THE HARMONIC OSCILLATOR The harmonic oscillator is a model which has several important applications in both classical and quantum mechanics. It serves as a prototype in the mathematical treatment
More informationSimple 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 informationCharge and Discharge of a Capacitor
Charge and Discharge of a Capacitor INTRODUCTION Capacitors 1 are devices that can store electric charge and energy. Capacitors have several uses, such as filters in DC power supplies and as energy storage
More informationR f. V i. ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response
ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response Objective: Design a practical differentiator circuit using common OP AMP circuits. Test the frequency response
More informationResponse 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 informationEstimating Dynamics for (DCmotor)+(1st Link) of the Furuta Pendulum
Estimating Dynamics for (DCmotor)+(1st Link) of the Furuta Pendulum 1 Anton and Pedro Abstract Here the steps done for identification of dynamics for (DCmotor)+(1st Link) of the Furuta Pendulum are described.
More informationStructural Resonance and Damping. Jake Lehman and Raisa Ebner. Advisor: Dr. Derin Sherman. Cornell College Department of Physics, Mount Vernon, IA
Lehman 1 Structural Resonance and Damping Jake Lehman and Raisa Ebner Advisor: Dr. Derin Sherman Cornell College Department of Physics, Mount Vernon, IA Introduction Earthquakes are very powerful and difficult
More informationPhysics 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 informationFXA 2008. UNIT G484 Module 2 4.2.3 Simple Harmonic Oscillations 11. frequency of the applied = natural frequency of the
11 FORCED OSCILLATIONS AND RESONANCE POINTER INSTRUMENTS Analogue ammeter and voltmeters, have CRITICAL DAMPING so as to allow the needle pointer to reach its correct position on the scale after a single
More informationSimple 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 informationEXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR CIRCUITS
EXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR CIRCUITS Equipment List S 1 BK Precision 4011 or 4011A 5 MHz Function Generator OS BK 2120B Dual Channel Oscilloscope V 1 BK 388B Multimeter L 1 Leeds &
More informationChapter 13. Mechanical Waves
Chapter 13 Mechanical Waves A harmonic oscillator is a wiggle in time. The oscillating object will move back and forth between +A and A forever. If a harmonic oscillator now moves through space, we create
More informationPrelab 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 informationboth 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 informationLab 5: Conservation of Energy
Lab 5: Conservation of Energy Equipment SWS, 1meter stick, 2meter stick, heavy duty bench clamp, 90cm rod, 40cm rod, 2 double clamps, brass spring, 100g mass, 500g mass with 5cm cardboard square
More informationSensor Performance Metrics
Sensor Performance Metrics Michael Todd Professor and Vice Chair Dept. of Structural Engineering University of California, San Diego mdtodd@ucsd.edu Email me if you want a copy. Outline Sensors as dynamic
More informationSIMPLE HARMONIC MOTION: SHIFTED ORIGIN AND PHASE
MISN026 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 informationOscillations: 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 informationPHYS2020: General Physics II Course Lecture Notes Section VII
PHYS2020: 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 informationChapter 14 Wave Motion
Query 17. If a stone be thrown into stagnating water, the waves excited thereby continue some time to arise in the place where the stone fell into the water, and are propagated from thence in concentric
More informationForced Oscillations in a Linear System
Forced Oscillations in a Linear System Manual Eugene Butikov Annotation. The manual includes a description of the simulated physical system and a summary of the relevant theoretical material for students
More informationExperiment P19: Simple Harmonic Motion  Mass on a Spring (Force Sensor, Motion Sensor)
PASCO scientific Physics Lab Manual: P191 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
More informationSimple 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
More information23.7. An Application of Fourier Series. Introduction. Prerequisites. Learning Outcomes
An Application of Fourier Series 23.7 Introduction In this Section we look at a typical application of Fourier series. The problem we study is that of a differential equation with a periodic (but nonsinusoidal)
More informationLecture 11 Chapter 16 Waves I
Lecture 11 Chapter 16 Waves I Forced oscillator from last time Slinky example Coiled wire Rope Transverse Waves demonstrator Longitudinal Waves magnetic balls Standing Waves machine Damped simple harmonic
More informationTorsion Pendulum. Life swings like a pendulum backward and forward between pain and boredom. Arthur Schopenhauer
Torsion Pendulum Life swings like a pendulum backward and forward between pain and boredom. Arthur Schopenhauer 1 Introduction Oscillations show up throughout physics. From simple spring systems in mechanics
More informationLab 5: Electromagnetic Induction: Faraday's Law
Lab 5: Electromagnetic Induction: Faraday's Law OBJECTIVE: To understand how changing magnetic fields can produce electric currents. To examine Lenz's Law and the derivative form of Faraday's Law. EQUIPMENT:
More informationManufacturing Equipment Modeling
QUESTION 1 For a linear axis actuated by an electric motor complete the following: a. Derive a differential equation for the linear axis velocity assuming viscous friction acts on the DC motor shaft, leadscrew,
More informationSimple Harmonic Motion
5 Simple Harmonic Motion Note: this section is not part of the syllabus for PHYS26. You should already be familiar with simple harmonic motion from your first year course PH115 Oscillations and Waves.
More informationFilters and Waveform Shaping
Physics 333 Experiment #3 Fall 211 Filters and Waveform Shaping Purpose The aim of this experiment is to study the frequency filtering properties of passive (R, C, and L) circuits for sine waves, and the
More informationInverted Pendulum Experiment
Introduction Inverted Pendulum Experiment This lab experiment consists of two experimental procedures, each with sub parts. Experiment 1 is used to determine the system parameters needed to implement a
More informationElectrical Resonance RLC circuits
Purpose: To investigate resonance phenomena that result from forced motion near a system's natural frequency. In this case the system will be a variety of RLC circuits. Theory: You are already familiar
More informationAR9161 B.Tech. VI Sem. Chemical Engineering Process Dynamics &Control Model Answer
AR9161 B.Tech. VI Sem. Chemical Engineering Process Dynamics &Control Model Answer Ans (1) Section A i. (A) ii. iii. iv. (B) (B) (B) v. (D) vi. vii. viii. ix. (C) (B) (B) (C) x. (A) Section B (1) (i)
More informationModeling of a detonation driven, linear electric generator facility
Modeling of a detonation driven, linear electric generator facility E.M. Braun, E. Baydar, and F.K. Lu 1 Introduction The pulsed detonation engine (PDE) has been developed over several decades due to the
More informationPHYS 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 informationChapter4: Superposition and Interference
Chapter4: Superposition and Interference Sections Superposition Principle Superposition of Sinusoidal Waves Interference of Sound Waves Standing Waves Beats: Interference in Time Nonsinusoidal Wave Patterns
More informationA B = AB sin(θ) = A B = AB (2) For two vectors A and B the cross product A B is a vector. The magnitude of the cross product
1 Dot Product and Cross Products For two vectors, the dot product is a number A B = AB cos(θ) = A B = AB (1) For two vectors A and B the cross product A B is a vector. The magnitude of the cross product
More informationActive Vibration Isolation of an Unbalanced Machine Spindle
UCRLCONF206108 Active Vibration Isolation of an Unbalanced Machine Spindle D. J. Hopkins, P. Geraghty August 18, 2004 American Society of Precision Engineering Annual Conference Orlando, FL, United States
More informationMeasurement of Equivalent Stiffness and Damping of Shock Absorbers
Measurement of Equivalent Stiffness and Damping of Shock Absorbers Mohan D. Rao a and Scott Gruenberg b a Mechanical EngineeringEngineering Mechanics Department b Keweenaw Research Center Michigan Technological
More informationPhys 2101 Gabriela González. A wave travels, but the particles producing the wave don t! Particles oscillate about a fixed mean position.
Phys 2101 Gabriela González A wave travels, but the particles producing the wave don t! Particles oscillate about a fixed mean position. 2 1 Assume a sinusoidal wave travels in the xdirection. At each
More informationANALYTICAL 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
More informationClass #12: Experiment The Exponential Function in Circuits, Pt 1
Class #12: Experiment The Exponential Function in Circuits, Pt 1 Purpose: The objective of this experiment is to begin to become familiar with the properties and uses of the exponential function in circuits
More informationChapter 18 4/14/11. Superposition Principle. Superposition and Interference. Superposition Example. Superposition and Standing Waves
Superposition Principle Chapter 18 Superposition and Standing Waves If two or more traveling waves are moving through a medium, the resultant value of the wave function at any point is the algebraic sum
More informationPhysics 1120: Waves Solutions
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Physics 1120: Waves Solutions 1. A wire of length 4.35 m and mass 137 g is under a tension of 125 N. What is the speed of a wave in this wire? If the tension
More informationSimple 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 informationWaves 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 informationActive Vibration Suppression of Sandwich Beams using Piezoelectric Shear Actuators
Advances in 2093 Active Vibration Suppression of Sandwich Beams using Piezoelectric Shear Actuators Senthil S. Vel 1, Brian P. Baillargeon 1 Summary This paper deals with the experimental and numerical
More informationState 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
More information