Math 240: Spring-Mass Systems
|
|
- Alexander Horton
- 5 years ago
- Views:
Transcription
1 Math 240: Spring-Mass Systems Ryan Blair University of Pennsylvania Wednesday December 5, 2012 Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
2 Outline 1 Today s Goals 2 Review 3 Spring-Mass Systems with Undamped Motion 4 Spring/Mass Systems with Damped Motion Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
3 Today s Goals Today s Goals 1 Learn how to solve spring/mass systems. Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
4 Review The Method of Undetermined Coefficients To solve a nonhomogeneous constant coefficient linear differential equation Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
5 Review The Method of Undetermined Coefficients To solve a nonhomogeneous constant coefficient linear differential equation 1 Step 1: Solve the associated homogeneous equation. Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
6 Review The Method of Undetermined Coefficients To solve a nonhomogeneous constant coefficient linear differential equation 1 Step 1: Solve the associated homogeneous equation. 2 Step 2: Find a particular solution by making a guess based on g(x). Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
7 Review The Method of Undetermined Coefficients To solve a nonhomogeneous constant coefficient linear differential equation 1 Step 1: Solve the associated homogeneous equation. 2 Step 2: Find a particular solution by making a guess based on g(x). 3 Step 3: Add the homogeneous solution and the particular solution together to get the general solution. Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
8 Spring-Mass Systems with Undamped Motion Spring-Mass Systems with Undamped Motion A flexible spring of length l 0 is suspended vertically from a rigid support. Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
9 Spring-Mass Systems with Undamped Motion Spring-Mass Systems with Undamped Motion A flexible spring of length l 0 is suspended vertically from a rigid support. A mass m is attached to its free end, the amount of stretch L 0 depends on the mass. Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
10 F s = kl 0 Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13 Spring-Mass Systems with Undamped Motion Spring-Mass Systems with Undamped Motion A flexible spring of length l 0 is suspended vertically from a rigid support. A mass m is attached to its free end, the amount of stretch L 0 depends on the mass. Hooke s Law: The spring exerts a restoring force F s opposite to the direction of elongation and proportional to the amount of elongation.
11 Spring-Mass Systems with Undamped Motion Newton s Second Law 1 The force due to gravity (F g = mg) is balanced by the restoring force kl 0 at the equilibrium position. mg = kl 0 Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
12 Spring-Mass Systems with Undamped Motion Newton s Second Law 1 The force due to gravity (F g = mg) is balanced by the restoring force kl 0 at the equilibrium position. mg = kl 0 2 If we displace from equilibrium by distance y the restoring force becomes k(y +L 0 ). Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
13 Spring-Mass Systems with Undamped Motion Newton s Second Law 1 The force due to gravity (F g = mg) is balanced by the restoring force kl 0 at the equilibrium position. mg = kl 0 2 If we displace from equilibrium by distance y the restoring force becomes k(y +L 0 ). Assuming free motion, Newton s Second Law states m d2 y dt 2 = k(l 0 +y)+mg = ky Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
14 Spring-Mass Systems with Undamped Motion Solutions to Undamped Spring Equation Question: What are the solutions to m d2 y +ky = 0? dt2 Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
15 Spring-Mass Systems with Undamped Motion Solutions to Undamped Spring Equation Question: What are the solutions to m d2 y +ky = 0? dt2 If ω0 2 = k m then the solutions are y(t) = c 1 cos(ω 0 t)+c 2 sin(ω 0 t). Example: A force of 400 newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/sec. Find the equation of motion. Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
16 Spring/Mass Systems with Damped Motion Spring/Mass Systems with Damped Motion Undamped motion is unrealistic. Instead assume we have a damping force proportional to the instantaneous velocity. Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
17 Spring/Mass Systems with Damped Motion Spring/Mass Systems with Damped Motion Undamped motion is unrealistic. Instead assume we have a damping force proportional to the instantaneous velocity. m d2 y dt +cdy 2 dt +ky = 0 is now our model, where m is the mass, k is the positive spring constant, c is the positive damping constant and y(t) is the position of the mass at time t. Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
18 Spring/Mass Systems with Damped Motion Changing Variables Let 2λ = c m and ω2 0 = k m. Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
19 Spring/Mass Systems with Damped Motion Changing Variables Let 2λ = c m and ω2 0 = k m. Then our damped motion D.E. becomes d 2 y dt +2λ dy 2 dt +ω2 0 y = 0 Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
20 Spring/Mass Systems with Damped Motion Changing Variables Let 2λ = c m and ω2 0 = k m. Then our damped motion D.E. becomes d 2 y dt +2λ dy 2 dt +ω2 0 y = 0 and the roots of the Aux. Equation become m 1 = λ+ λ 2 ω0 2 and m 2 = λ λ 2 ω0 2 Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
21 Spring/Mass Systems with Damped Motion Case 1: Overdamped If λ 2 ω0 2 > 0 the system is overdamped since c is large when compared to k. In this case the solution is y = e λt (c 1 e λ2 ω0 2t +c 2 e λ2 ω0 2t ). Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
22 Spring/Mass Systems with Damped Motion Case 2: Critically Damped If λ 2 ω0 2 = 0 the system is critically damped since a slight decrease in the damping force would result in oscillatory motion. In this case the solution is y = e λt (c 1 +c 2 t) Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
23 Spring/Mass Systems with Damped Motion Case 3: Underdamped If λ 2 ω0 2 < 0 the system is underdamped since k is large when compared to c. In this case the solution is. y = e λt (c 1 cos( ω0 2 λ2 t)+c 2 sin( ω0 2 λ2 t)) Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
24 Example Spring/Mass Systems with Damped Motion A 4 meter spring measures 8 meters long after a force of 16 newtons acts to it. A mass of 8 kilograms is attached to the spring. The medium through which the mass moves offers a damping force equal to 2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 5 meters/sec. Ryan Blair (U Penn) Math 240: Spring-Mass Systems Wednesday December 5, / 13
EGR/MA265, Math Tools for Engineering Problem Solving Final Exam, 2013
EGR/MA265, Math Tools for Engineering Problem Solving Final Exam, 2013 Name and section: Instructors name: 1. Do not open this exam until you are told to do so. 2. This exam has 14 pages including this
More informationω d = driving frequency, F m = amplitude of driving force, b = damping constant and ω = natural frequency of undamped, undriven oscillator.
Physics 121H Fall 2015 Homework #14 16-November-2015 Due Date : 23-November-2015 Reading : Chapter 15 Note: Problems 7 & 8 are tutorials dealing with damped and driven oscillations, respectively. It may
More informationChapter 14 Oscillations. Copyright 2009 Pearson Education, Inc.
Chapter 14 Oscillations 14-7 Damped Harmonic Motion Damped harmonic motion is harmonic motion with a frictional or drag force. If the damping is small, we can treat it as an envelope that modifies the
More information3/23/2015. Chapter 11 Oscillations and Waves. Contents of Chapter 11. Contents of Chapter Simple Harmonic Motion Spring Oscillations
Lecture PowerPoints Chapter 11 Physics: Principles with Applications, 7 th edition Giancoli Chapter 11 and Waves This work is protected by United States copyright laws and is provided solely for the use
More informationA Differential Look at the Watt s Governor
Differential Equations Spring 2003 1/25 A Differential Look at the Watt s Governor by Tim Honn & Seth Stone College of the Redwoods Eureka,CA Math dept. email: timhonn@cox.net email: lamentofseth@hotmail.com
More informationCHAPTER 11 TEST REVIEW -- MARKSCHEME
AP PHYSICS Name: Period: Date: 50 Multiple Choice 45 Single Response 5 Multi-Response Free Response 3 Short Free Response 2 Long Free Response MULTIPLE CHOICE DEVIL PHYSICS BADDEST CLASS ON CAMPUS AP EXAM
More informationModule 7 : Design of Machine Foundations. Lecture 31 : Basics of soil dynamics [ Section 31.1: Introduction ]
Lecture 31 : Basics of soil dynamics [ Section 31.1: Introduction ] Objectives In this section you will learn the following Dynamic loads Degrees of freedom Lecture 31 : Basics of soil dynamics [ Section
More informationExperiment P20: Driven Harmonic Motion - Mass on a Spring (Force Sensor, Motion Sensor, Power Amplifier)
PASCO scientific Physics Lab Manual: P20-1 Experiment P20: - Mass on a Spring (Force Sensor, Motion Sensor, Power Amplifier) Concept Time SW Interface Macintosh file Windows file harmonic motion 45 m 700
More informationExam 1 Study Guide. Math 223 Section 12 Fall Student s Name
Exam 1 Study Guide Math 223 Section 12 Fall 2015 Dr. Gilbert Student s Name The following problems are designed to help you study for the first in-class exam. Problems may or may not be an accurate indicator
More informationExperiment 1 LRC Transients
Physics 263 Experiment 1 LRC Transients 1 Introduction In this experiment we will study the damped oscillations and other transient waveforms produced in a circuit containing an inductor, a capacitor,
More informationExperiment P10: Acceleration of a Dynamics Cart II (Motion Sensor)
PASCO scientific Physics Lab Manual: P10-1 Experiment P10: (Motion Sensor) Concept Time SW Interface Macintosh file Windows file Newton s Laws 30 m 500 or 700 P10 Cart Acceleration II P10_CAR2.SWS EQUIPMENT
More informationOscillations II: Damped and/or Driven Oscillations
Oscillations II: Damped and/or Driven Oscillations Michael Fowler 3/4/9 Introducing Damping We ll assume the damping force is proportional to the velocity, and, of course, in the opposite direction. Then
More informationChapter 8. Natural and Step Responses of RLC Circuits
Chapter 8. Natural and Step Responses of RLC Circuits By: FARHAD FARADJI, Ph.D. Assistant Professor, Electrical Engineering, K.N. Toosi University of Technology http://wp.kntu.ac.ir/faradji/electriccircuits1.htm
More information1) The time for one cycle of a periodic process is called the A) period. B) frequency. C) wavelength. D) amplitude.
Practice quiz for engineering students. Real test next Tuesday. Plan on an essay/show me work question as well. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers
More informationPHY1 Review for Exam 9. Equations. V = 2πr / T a c = V 2 /r. W = Fdcosθ PE = mgh KE = ½ mv 2 E = PE + KE
Topics Simple Harmonic Motion Springs Pendulums Waves Transverse Longitudinal Pulse Continuous Interference Refraction Diffraction Equations V = 2πr / T a c = V 2 /r F = ma F F = µf N W = Fdcosθ PE = mgh
More informationCONTENTS. Cambridge University Press Vibration of Mechanical Systems Alok Sinha Table of Contents More information
CONTENTS Preface page xiii 1 Equivalent Single-Degree-of-Freedom System and Free Vibration... 1 1.1 Degrees of Freedom 3 1.2 Elements of a Vibratory System 5 1.2.1 Mass and/or Mass-Moment of Inertia 5
More informationExperiment P11: Newton's Second Law Constant Force (Force Sensor, Motion Sensor)
PASCO scientific Physics Lab Manual: P11-1 Experiment P11: Newton's Second Law Constant Force (Force Sensor, Motion Sensor) Concept Time SW Interface Macintosh file Windows file Newton s Laws 30 m 500
More informationActivity P40: Driven Harmonic Motion - Mass on a Spring (Force Sensor, Motion Sensor, Power Amplifier)
Name Class Date Activity P40: Driven Harmonic Motion - Mass on a Spring (Force Sensor, Motion Sensor, Power Amplifier) Concept DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) Harmonic motion P40
More informationVersion 001 HW#1 - Vibrations & Waves arts (00224) 1
Version HW# - Vibrations & Waves arts (4) This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Superposition. points
More informationLab 11. Speed Control of a D.C. motor. Motor Characterization
Lab 11. Speed Control of a D.C. motor Motor Characterization Motor Speed Control Project 1. Generate PWM waveform 2. Amplify the waveform to drive the motor 3. Measure motor speed 4. Estimate motor parameters
More informationAE2610 Introduction to Experimental Methods in Aerospace
AE2610 Introduction to Experimental Methods in Aerospace Lab #3: Dynamic Response of a 3-DOF Helicopter Model C.V. Di Leo 1 Lecture/Lab learning objectives Familiarization with the characteristics of dynamical
More informationD102. Damped Mechanical Oscillator
D10. Damped Mechanical Oscillator Aim: design and writing an application for investigation of a damped mechanical oscillator Measurements of free oscillations of a damped oscillator Measurements of forced
More informationEE 42/100: Lecture 8. 1 st -Order RC Transient Example, Introduction to 2 nd -Order Transients. EE 42/100 Summer 2012, UC Berkeley T.
EE 42/100: Lecture 8 1 st -Order RC Transient Example, Introduction to 2 nd -Order Transients Circuits with non-dc Sources Recall that the solution to our ODEs is Particular solution is constant for DC
More informationExperiment VI: The LRC Circuit and Resonance
Experiment VI: The ircuit and esonance I. eferences Halliday, esnick and Krane, Physics, Vol., 4th Ed., hapters 38,39 Purcell, Electricity and Magnetism, hapter 7,8 II. Equipment Digital Oscilloscope Digital
More informationLecture 19. Vector fields. Dan Nichols MATH 233, Spring 2018 University of Massachusetts. April 10, 2018.
Lecture 19 Vector fields Dan Nichols nichols@math.umass.edu MATH 233, Spring 218 University of Massachusetts April 1, 218 (2) Chapter 16 Chapter 12: Vectors and 3D geometry Chapter 13: Curves and vector
More informationThe period is the time required for one complete oscillation of the function.
Trigonometric Curves with Sines & Cosines + Envelopes Terminology: AMPLITUDE the maximum height of the curve For any periodic function, the amplitude is defined as M m /2 where M is the maximum value and
More informationMAE106 Laboratory Exercises Lab # 5 - PD Control of DC motor position
MAE106 Laboratory Exercises Lab # 5 - PD Control of DC motor position University of California, Irvine Department of Mechanical and Aerospace Engineering Goals Understand how to implement and tune a PD
More informationGet Solution of These Packages & Learn by Video Tutorials on EXERCISE-1
EXERCISE-1 SECTION (A) : EQUATION OF TRAVELLING WAVE (INCLUDING SINE WAVE) A 1. The wave function for a traveling wave on a taut string is (in SI units) s(x, t) = (0.350 m) sin (10πt 3πx + π/4) (a) What
More informationSection 5.2 Graphs of the Sine and Cosine Functions
Section 5.2 Graphs of the Sine and Cosine Functions We know from previously studying the periodicity of the trigonometric functions that the sine and cosine functions repeat themselves after 2 radians.
More informationLAB 10: OSCILLATIONS AND SOUND
159 Name Date Partners LAB 10: OSCILLATIONS AND SOUND (Image from http://archive.museophile.org/sound/) OBJECTIVES To understand the effects of damping on oscillatory motion. To recognize the effects of
More information1. Introduction. 2. Concept. reflector. transduce r. node. Kraftmessung an verschiedenen Fluiden in akustischen Feldern
1. Introduction The aim of this Praktikum is to familiarize with the concept and the equipment of acoustic levitation and to measure the forces exerted by an acoustic field on small spherical objects.
More informationStandingWaves_P2 [41 marks]
StandingWaves_P2 [41 marks] A loudspeaker emits sound towards the open end of a pipe. The other end is closed. A standing wave is formed in the pipe. The diagram represents the displacement of molecules
More informationCharacterizing the Frequency Response of a Damped, Forced Two-Mass Mechanical Oscillator
Characterizing the Frequency Response of a Damped, Forced Two-Mass Mechanical Oscillator Shanel Wu Harvey Mudd College 3 November 013 Abstract A two-mass oscillator was constructed using two carts, springs,
More informationEECS40 RLC Lab guide
EECS40 RLC Lab guide Introduction Second-Order Circuits Second order circuits have both inductor and capacitor components, which produce one or more resonant frequencies, ω0. In general, a differential
More informationABC Math Student Copy
Page 1 of 17 Physics Week 9(Sem. 2) Name Chapter Summary Waves and Sound Cont d 2 Principle of Linear Superposition Sound is a pressure wave. Often two or more sound waves are present at the same place
More informationWaves and Sound Practice Test 43 points total Free- response part: [27 points]
Name Waves and Sound Practice Test 43 points total Free- response part: [27 points] 1. To demonstrate standing waves, one end of a string is attached to a tuning fork with frequency 120 Hz. The other end
More informationIntermediate and Advanced Labs PHY3802L/PHY4822L
Intermediate and Advanced Labs PHY3802L/PHY4822L Torsional Oscillator and Torque Magnetometry Lab manual and related literature The torsional oscillator and torque magnetometry 1. Purpose Study the torsional
More informationEC6405 - CONTROL SYSTEM ENGINEERING Questions and Answers Unit - II Time Response Analysis Two marks 1. What is transient response? The transient response is the response of the system when the system
More informationSPH4U UNIVERSITY PHYSICS
09/09/0 SPH4U UNIVERSITY PHYSICS DYNAMICS L Atwood s Machine & Fletcher s Trolley (P.~) Connected Objects Elevators are not simply suspended from cables. Instead, the supporting cable passes up over a
More informationPoles and Zeros of H(s), Analog Computers and Active Filters
Poles and Zeros of H(s), Analog Computers and Active Filters Physics116A, Draft10/28/09 D. Pellett LRC Filter Poles and Zeros Pole structure same for all three functions (two poles) HR has two poles and
More informationEE 42/100 Lecture 18: RLC Circuits. Rev A 3/17/2010 (3:48 PM) Prof. Ali M. Niknejad
A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 18 p. 1/19 EE 42/100 Lecture 18: RLC Circuits ELECTRONICS Rev A 3/17/2010 (3:48 PM) Prof. Ali M. Niknejad University of California,
More information#8A RLC Circuits: Free Oscillations
#8A RL ircuits: Free Oscillations Goals In this lab we investigate the properties of a series RL circuit. Such circuits are interesting, not only for there widespread application in electrical devices,
More informationSlinky vs. guitar. W.E. Bailey, APAM/MSE EN1102
Slinky vs. guitar W.E. Bailey, APAM/MSE EN1102 Differential spring element Figure: Differential length dx of spring under tension T with curvature is not a constant. θ = θ(x) W.E. Bailey, APAM/MSE EN1102
More informationConventional geophone topologies and their intrinsic physical limitations, determined
Magnetic innovation in velocity sensing Low -frequency with passive Conventional geophone topologies and their intrinsic physical limitations, determined by the mechanical construction, limit their velocity
More informationPhysics 132 Quiz # 23
Name (please (please print) print) Physics 132 Quiz # 23 I. I. The The current in in an an ac ac circuit is is represented by by a phasor.the value of of the the current at at some time time t t is is
More informationLAB 12: OSCILLATIONS AND SOUND
193 Name Date Partners LAB 12: OSCILLATIONS AND SOUND Animals can hear over a wider frequency range of humans, but humans can hear over a wide frequency from 20 Hz to 20,000 Hz (Image from http://archive.museophile.org/sound/)
More information1. Transverse Waves: the particles in the medium move perpendicular to the direction of the wave motion
Mechanical Waves Represents the periodic motion of matter e.g. water, sound Energy can be transferred from one point to another by waves Waves are cyclical in nature and display simple harmonic motion
More information[ á{tå TÄàt. Chapter Four. Time Domain Analysis of control system
Chapter Four Time Domain Analysis of control system The time response of a control system consists of two parts: the transient response and the steady-state response. By transient response, we mean that
More informationDynamic Vibration Absorber
Part 1B Experimental Engineering Integrated Coursework Location: DPO Experiment A1 (Short) Dynamic Vibration Absorber Please bring your mechanics data book and your results from first year experiment 7
More informationFORCED HARMONIC MOTION Ken Cheney
FORCED HARMONIC MOTION Ken Cheney ABSTRACT The motion of an object under the influence of a driving force, a restoring force, and a friction force is investigated using a mass on a spring driven by a variable
More informationPhysics 140 Winter 2014 April 21. Wave Interference and Standing Waves
Physics 140 Winter 2014 April 21 Wave Interference and Standing Waves 1 Questions concerning today s youtube video? 3 Reflections A sinusoidal wave is generated by shaking one end (x = L) of a fixed string
More information22.19 To determine the wavelength, use the fact that the speed of a wave is equal to its wavelength times its frequency
hhh.schaums.22.19_22.28 22.19 To determine the wavelength, use the fact that the speed of a wave is equal to its wavelength times its frequency or speed = waveln gth frequency speed is in m/s, wavelength
More informationStanding Waves + Reflection
Standing Waves + Reflection Announcements: Will discuss reflections of transverse waves, standing waves and speed of sound. We will be covering material in Chap. 16. Plan to review material on Wednesday
More informationCalifornia University of Pennsylvania Department of Applied Engineering & Technology Electrical Engineering Technology
California University of Pennsylvania Department of Applied Engineering & Technology Electrical Engineering Technology < Use as a guide Do not copy and paste> EET 410 Design of Feedback Control Systems
More informationMATH Exam 2 Solutions November 16, 2015
MATH 1.54 Exam Solutions November 16, 15 1. Suppose f(x, y) is a differentiable function such that it and its derivatives take on the following values: (x, y) f(x, y) f x (x, y) f y (x, y) f xx (x, y)
More informationPre Test 1. Name. a Hz b Hz c Hz d Hz e Hz. 1. d
Name Pre Test 1 1. The wavelength of light visible to the human eye is on the order of 5 10 7 m. If the speed of light in air is 3 10 8 m/s, find the frequency of the light wave. 1. d a. 3 10 7 Hz b. 4
More informationThe units of vibration depend on the vibrational parameter, as follows:
Vibration Measurement Vibration Definition Basically, vibration is oscillating motion of a particle or body about a fixed reference point. Such motion may be simple harmonic (sinusoidal) or complex (non-sinusoidal).
More informationFinal Reg Wave and Sound Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Final Reg Wave and Sound Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) What is the frequency of a 2.5 m wave traveling at 1400 m/s? 1) 2)
More informationOn the axes of Fig. 4.1, sketch the variation with displacement x of the acceleration a of a particle undergoing simple harmonic motion.
1 (a) (i) Define simple harmonic motion. (b)... On the axes of Fig. 4.1, sketch the variation with displacement x of the acceleration a of a particle undergoing simple harmonic motion. Fig. 4.1 A strip
More information, answer the next six questions.
Frequency Response Problems Conceptual Questions 1) T/F Given f(t) = A cos (ωt + θ): The amplitude of the output in sinusoidal steady-state increases as K increases and decreases as ω increases. 2) T/F
More informationBarrier. (a) State the conditions which must be met for an object to move with simple harmonic motion. (2)
1 In a television game show contestants have to pass under a barrier. The barrier has a vertical height of 0.70m and moves up and down with simple harmonic motion. 3.0m Barrier 0.70m (a) State the conditions
More informationVibratory Feeder Bowl Analysis
The Journal of Undergraduate Research Volume 7 Journal of Undergraduate Research, Volume 7: 2009 Article 7 2009 Vibratory Feeder Bowl Analysis Chris Green South Dakota State University Jeff Kreul South
More informationWaves are generated by an oscillator which has to be powered.
Traveling wave is a moving disturbance. Can transfer energy and momentum from one place to another. Oscillations occur simultaneously in space and time. Waves are characterized by 1. their velocity 2.
More informationEXPERIMENT 8: LRC CIRCUITS
EXPERIMENT 8: LRC 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 & Northrup #1532 100 mh Inductor
More informationWhen you bring it in, please take a digital picture of it and post it on your web page.
Mobile The GOAL of this project is for you to design and build a balanced hanging mobile using the physical relationships of a system in equilibrium. You will, individually, build a mobile that will consist
More informationMagnitude & Intensity
Magnitude & Intensity Lecture 7 Seismometer, Magnitude & Intensity Vibrations: Simple Harmonic Motion Simplest vibrating system: 2 u( x) 2 + ω u( x) = 0 2 t x Displacement u ω is the angular frequency,
More informationMidterm 1. Total. Name of Student on Your Left: Name of Student on Your Right: EE 20N: Structure and Interpretation of Signals and Systems
EE 20N: Structure and Interpretation of Signals and Systems Midterm 1 12:40-2:00, February 19 Notes: There are five questions on this midterm. Answer each question part in the space below it, using the
More informationPhysics Lab 2.2: Tug-of-War
Physics Lab 2.2: Tug-of-War Name Period Purpose: To investigate the tension in a string, the function of a simple pulley, and a simple tug-of-war. Materials: 1 75 cm string 2 30-cm strings 1000 g of assorted
More informationQuarterly Progress and Status Report. The bouncing bow: Some important parameters
Dept. for Speech, Music and Hearing Quarterly Progress and Status Report The bouncing bow: Some important parameters Askenfelt, A. and Guettler, K. journal: TMH-QPSR volume: 38 number: 2-3 year: 1997 pages:
More informationPhysics 351 Wednesday, February 7, 2018
Physics 351 Wednesday, February 7, 2018 HW3 due Friday. You finished reading ch7 last weekend. You ll read ch8 (Kepler problem) this weekend. HW help: Bill is in DRL 3N6 Wednesdays 4pm 7pm. Grace is in
More informationSystem Inputs, Physical Modeling, and Time & Frequency Domains
System Inputs, Physical Modeling, and Time & Frequency Domains There are three topics that require more discussion at this point of our study. They are: Classification of System Inputs, Physical Modeling,
More informationWe are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors
We are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists 3,900 116,000 120M Open access books available International authors and editors Downloads Our
More informationSound, acoustics Slides based on: Rossing, The science of sound, 1990.
Sound, acoustics Slides based on: Rossing, The science of sound, 1990. Acoustics 1 1 Introduction Acoustics 2! The word acoustics refers to the science of sound and is a subcategory of physics! Room acoustics
More informationModule 2 WAVE PROPAGATION (Lectures 7 to 9)
Module 2 WAVE PROPAGATION (Lectures 7 to 9) Lecture 9 Topics 2.4 WAVES IN A LAYERED BODY 2.4.1 One-dimensional case: material boundary in an infinite rod 2.4.2 Three dimensional case: inclined waves 2.5
More informationUIC PHYSICS 105 Fall 2014 Final Exam
UIC: Physics 105 Final Exam Fall 2014 Wednesday, December 10 # LAST Name (print) FIRST Name (print) Signature: UIN #: Giving or receiving aid in any examination is cause for dismissal from the University.
More informationUse of the logarithmic decrement to assess the damping in oscillations
Revista de Investigación de Física 19, 161901551 (2016) Use of the logarithmic decrement to assess the damping in oscillations Javier Montenegro Joo 1,2 1 Facultad de Ciencias Físicas, Universidad Nacional
More informationDetermining the Relationship Between the Range and Initial Velocity of an Object Moving in Projectile Motion
Determining the Relationship Between the Range and Initial Velocity of an Object Moving in Projectile Motion Sadaf Fatima, Wendy Mixaynath October 07, 2011 ABSTRACT A small, spherical object (bearing ball)
More informationMusic: Sound that follows a regular pattern; a mixture of frequencies which have a clear mathematical relationship between them.
The Sound of Music Music: Sound that follows a regular pattern; a mixture of frequencies which have a clear mathematical relationship between them. How is music formed? By STANDING WAVES Formed due to
More informationExperiment 3 Topic: Dynamic System Response Week A Procedure
Experiment 3 Topic: Dynamic System Response Week A Procedure Laboratory Assistant: Email: Office Hours: LEX-3 Website: Brock Hedlund bhedlund@nd.edu 11/05 11/08 5 pm to 6 pm in B14 http://www.nd.edu/~jott/measurements/measurements_lab/e3
More informationVibration of Mechanical Systems
Vibration of Mechanical Systems This is a textbook for a first course in mechanical vibrations. There are many books in this area that try to include everything, thus they have become exhaustive compendiums
More informationExam Signal Detection and Noise
Exam Signal Detection and Noise Tuesday 27 January 2015 from 14:00 until 17:00 Lecturer: Sense Jan van der Molen Important: It is not allowed to use a calculator. Complete each question on a separate piece
More information3) For vibrational motion, the maximum displacement from the equilibrium point is called the
WAVES & SOUND Conceptual Questions 1) The time for one cycle of a periodic process is called the 2) For a periodic process, the number of cycles per unit time is called the 3) For vibrational motion, the
More information5.3-The Graphs of the Sine and Cosine Functions
5.3-The Graphs of the Sine and Cosine Functions Objectives: 1. Graph the sine and cosine functions. 2. Determine the amplitude, period and phase shift of the sine and cosine functions. 3. Find equations
More informationDate: Current Balance. In this lab, you will examine the interaction of two current carrying wires.
Name: Partner(s): Date: Current Balance Purpose In this lab, you will examine the interaction of two current carrying wires. Significance The ampere, in the MKS system of units, is defined in the following
More informationMake-Up Labs Next Week Only
Make-Up Labs Next Week Only Monday, Mar. 30 to Thursday, April 2 Make arrangements with Dr. Buntar in BSB-B117 If you have missed a lab for any reason, you must complete the lab in make-up week. Energy;
More informationPreliminary study of the vibration displacement measurement by using strain gauge
Songklanakarin J. Sci. Technol. 32 (5), 453-459, Sep. - Oct. 2010 Original Article Preliminary study of the vibration displacement measurement by using strain gauge Siripong Eamchaimongkol* Department
More informationPhysics Jonathan Dowling. Lecture 35: MON 16 NOV Electrical Oscillations, LC Circuits, Alternating Current II
hysics 2113 Jonathan Dowling Lecture 35: MON 16 NOV Electrical Oscillations, LC Circuits, Alternating Current II Damped LCR Oscillator Ideal LC circuit without resistance: oscillations go on forever; ω
More informationApplication Note #2442
Application Note #2442 Tuning with PL and PID Most closed-loop servo systems are able to achieve satisfactory tuning with the basic Proportional, Integral, and Derivative (PID) tuning parameters. However,
More informationMotion Lab : Relative Speed. Determine the Speed of Each Car - Gathering information
Motion Lab : Introduction Certain objects can seem to be moving faster or slower based on how you see them moving. Does a car seem to be moving faster when it moves towards you or when it moves to you
More informationpoint at zero displacement string 80 scale / cm Fig. 4.1
1 (a) Fig. 4.1 shows a section of a uniform string under tension at one instant of time. A progressive wave of wavelength 80 cm is moving along the string from left to right. At the instant shown, the
More informationA Wheeling-Hopping Combination Scout Robot
A Wheeling-Hopping Combination Scout Robot Jie Zhao, Gangfeng Liu, Qinghu Han, and Hegao Cai State Key Laboratory of Robotic Technology and System,Harbin Institute of Technology, Harbin, 151, P. R. China
More informationExercise 4: 2.order Systems (Solutions)
Exercise 4: 2.order Systems (Solutions) A second order transfer function is given on the form: Where is the gain zeta is the relative damping factor [rad/s] is the undamped resonance frequency. The value
More informationName: Period: Date: Math Lab: Explore Transformations of Trig Functions
Name: Period: Date: Math Lab: Explore Transformations of Trig Functions EXPLORE VERTICAL DISPLACEMENT 1] Graph 2] Explain what happens to the parent graph when a constant is added to the sine function.
More informationResonance Tube. 1 Purpose. 2 Theory. 2.1 Air As A Spring. 2.2 Traveling Sound Waves in Air
Resonance Tube Equipment Capstone, complete resonance tube (tube, piston assembly, speaker stand, piston stand, mike with adapters, channel), voltage sensor, 1.5 m leads (2), (room) thermometer, flat rubber
More informationPC1141 Physics I Standing Waves in String
PC1141 Physics I Standing Waves in String 1 Purpose Determination the length of the wire L required to produce fundamental resonances with given frequencies Demonstration that the frequencies f associated
More informationElectronics and Instrumentation Name ENGR-4220 Fall 1999 Section Modeling the Cantilever Beam Supplemental Info for Project 1.
Name ENGR-40 Fall 1999 Section Modeling the Cantilever Beam Supplemental Info for Project 1 The cantilever beam has a simple equation of motion. If we assume that the mass is located at the end of the
More informationLC Resonant Circuits Dr. Roger King June Introduction
LC Resonant Circuits Dr. Roger King June 01 Introduction Second-order systems are important in a wide range of applications including transformerless impedance-matching networks, frequency-selective networks,
More informationWhat is a Sine Function Graph? U4 L2 Relate Circle to Sine Activity.pdf
Math 3 Unit 6, Trigonometry L04: Amplitude and Period of Sine and Cosine AND Translations of Sine and Cosine Functions WIMD: What I must do: I will find the amplitude and period from a graph of the sine
More informationAlgebra and Trig. I. The graph of
Algebra and Trig. I 4.5 Graphs of Sine and Cosine Functions The graph of The graph of. The trigonometric functions can be graphed in a rectangular coordinate system by plotting points whose coordinates
More informationME scope Application Note 02 Waveform Integration & Differentiation
ME scope Application Note 02 Waveform Integration & Differentiation The steps in this Application Note can be duplicated using any ME scope Package that includes the VES-3600 Advanced Signal Processing
More information