Time [seconds]
|
|
- Lucas Lee
- 5 years ago
- Views:
Transcription
1 .003 Fall 1999 Solution of Homework Aignment 4 1. Due to the application of a 1.0 Newton tep-force, the ytem ocillate at it damped natural frequency! d about the new equilibrium poition y k =. From the given Diplacement Repone plot, the equilibrium oet can be etimated to be = 4.4 x 10,4 meter. The damped natural frequency can be etimated by counting the cycle, 10, in.0 econd, which give a damped period T d =0: econd, and! d ==T d = 31:4 rad/ec. The logarithmic decrement LDR can be etimated by meauring the ratio of ucceive peak amplitude. Thi i generally a dicult meaurement tomake accurately. One way to increae the accuracy i to make a large number of meaurement baed on dierent pair of ucceive peak, and average the reult. Draw a line acro the plot at y =and meaure the amplitude of everal peak. Since only the ratio of ucceive peak will be ued, the meaurement can be in term of any convenient length unit. The meaurement below are in millimeter. Station Amplitude Ratio 0 6:, 1 4:86 0:781 4:00 0:83 3 3:08 0:770 4 :56 0: :94 0: :68 0:866 The average of thee rt ix ratio i 0.805, o the etimate for the LDR i ln 0:805 =,0:17. (a) The etimated tine i k = f a = 1:0 = 70 Newton/meter 4:4 10,4 (b) To etimate the ma m, when the tine k i known, it i neceary to know the undamped natural frequency! o. At thi point we know only the damped natural frequency! d. We can potpone etimation of the ma m until the damping ratio i etimated in (c) below, or we can aume, ince more than ten cycle of ocillation are viible, that the damping i uciently light to permit u to make the approximation that! o! d, in which cae m k! d = 70 =:30 kg (31:4) (c) To etimate the damping parameter b, we need to know the damping ratio. The damping ratio follow from the log decrement ratio, LDR, according to the formula = LDR + LDR
2 given in the Note accompanying Lecture 6. Inertion of the etimation LDR =,0:17 yield 0:069. (Note: With thi value of the undamped natural frequency i etimated a follow! p d 1, 31:4 q =31:5 rad/ec 1, (0:069) With thi etimate for! o the ma m, previouly etimated in (b) above at.30 kg, would now be etimated to be.9 kg. The damping parameter b i then etimated a b =! o m (0:069)(31:5)(:9) = 9:95 kg/ec, or 9.95 N/m/ec. With two plate-on-pring unit face-to-face, the eective tine of the combined ytem i k = 1000 N/m, and the eective damping parameter i b = 10 N/m/ec. For free vertical motion of the ma m =:0 kg, the diplacement y k from the equilibrium poition of the model atie the equation m d y k dt + bdy k dt + ky k =0 (a) The undamped natural frequency! o for the model i (b) The damping ratio for the model i k 1000 m = =:4 rad/ec, or f o =! o = (c) The decay time contant for the model i = 1! o = b! o m = 10 (:4)() =0: (0:1116)(:4) =0:400ec =3:56 Hz 3. Initially the bungee jumper free-fall under the inuence of gravity and air reitance, then when the lack i taken up in the elatic cord, the cord exert an increaing retarding force which reduce her velocity to zero at level A, after which he bob up and down with decreaing amplitude until he come to ret at the equilibrium poition at level B. For the purpoe of a preliminary etimate of the condition up to intant at which level A i reached, neglect the eect of air reitance and damping in the cord. Under thi aumption energy i conerved. In the rt jump the equilibrium poition B i 0 feet below the point where the cord begin to tretch. The tine of the cord i then etimated a k = W = =7:5pound/foot
3 The undamped natural frequency of the ma-pring ytem coniting of the jumper and cord i k k 7:5 m = W=g = =1:69 rad/ec 150=3: Let the elevation of the upper attachment point of the cord be denoted by h o, the elevation of the point where the lack i taken up and the cord begin to tretch be enoted by h 1, the elevation of the equilibrium point B be denoted by h B, and the elevation of the point A where the jumper' velocity rt vanihe be denoted by h A. (a) In the rt jump, h o, h 1 = 100 feet, and h o, h B = 10 feet. The level A can be located by equating the potential energy lot in the fall to the elatic energy in the cord. W (h o, h A )=k(h o, h A )= 1 k(h1,h A) = 1 k[(h o, h A ), 100] Thi reduce to a quadratic equation for (h o, h A ) whoe olution are (h o, h A ) = 10 66:3 feet The phyically ignicant rooti(h o,h A ) = 186:3 feet. The low point A i 66.3 feet below the equilibrium level B, or feet below the upper attachment point. (b) The maximum downward acceleration i 3. feet/ec fall. during the initial free (c) The maximum upward acceleration occur at point A and i a max = (Max diplacement from equilibrium)! o = (66:3)(1:69) = 106:8ft/ec which i 3.3 time the acceleration of gravity. (d) The primary aumption made i that diipation of energy ha been neglected. The cord ha been aumed to behave like a linear pring. (e) In the econd jump the lack length i doubled which cut the tine in half, and double the ditance to 40 feet. The natural frequency i reduced to rad/ec. The location of the new low point A' i obtained by olving a imilar quadratic equation with the new value of h 0, h 1 = 00 feet, h o, h B 0 = 40 feet, and = 40 feet. The reult i (h o, h A 0) = 40 13:7 feet The phyically ignicant rooti(h o,h A ) = 373 feet. The low point A i 13.7 feet below the equilibrium level B', or 373 feet below the upper attachment point.
4 (f) The level of the equilibrium point B' i 40 feet below the attachment point. (g) The maximum downward acceleration i till 3, feet/ec (h) The maximum upward acceleration i a max = (Max diplacement from equilibrium)! o = (13:7)(0:897) = 106:8ft/ec Although the jump involve a longer free fall and a greater extenion of the cord the maximum acceleration doe not change! 400 Bungee Jump Level B Elevation [feet] Level A Level B Level A Time [econd] Figure 1: Time Hitorie of Bungee Jump (i) The time hitorie of the two jump are hown in Fig.1. For plotting purpoe the elevation of the upper attachment point wa (arbitrarily) aigned the value 400 feet. The trajectory of free fall i indicated by the dahed-line parabola.
5 With 100 feet of lack the jumper' trajectory depart from the free-fall parabola at h = 300 ft and begin to ocillate about the nal equilibrium level B. With no damping the maximum excurion (and maximum acceleration) i at Level A. With 00 feet of lack the jumper' trajectory depart from the free-fall parabola at h = 00 ft and begin to ocillate about the nal equilibrium level B1. With no damping the maximum excurion (and maximum acceleration) i at Level A1. 4. Let x be the diplacement of the engine with repect to the tationary crate. The eective tine of the two end element i k, and the eective damping parameter i b. (a) The equation of motion for the engine i m d x dt +bdx dt +kx =0 (b) The engine weight i W = 500 pound. It ma i m = W=g. The value of k and b can be deduced from the given value of damped natural frequency! d =and damping ratio =0:707 from the equation! o =! d 1, = k W=g The undamped natural frequency i and b =! o W=g q 1, (0; 707) =8:88 rad/ec and k = W! o g The damping parameter i = (500)(8:88) (386) = 51: pound/inch W b =! o g =(0:707)(8:88)500 =8:13 pound/in/ec 386
ME 375 EXAM #1 Tuesday February 21, 2006
ME 375 EXAM #1 Tueday February 1, 006 Diviion Adam 11:30 / Savran :30 (circle one) Name Intruction (1) Thi i a cloed book examination, but you are allowed one 8.5x11 crib heet. () You have one hour to
More informationThese are practice problems for the final exam. You should attempt all of them, but turn in only the even-numbered problems!
Math 33 - ODE Due: 7 December 208 Written Problem Set # 4 Thee are practice problem for the final exam. You hould attempt all of them, but turn in only the even-numbered problem! Exercie Solve the initial
More informationProf. Dr. Ibraheem Nasser Examples_6 October 13, Review (Chapter 6)
Prof. Dr. Ibraheem Naer Example_6 October 13, 017 Review (Chapter 6) cceleration of a loc againt Friction (1) cceleration of a bloc on horizontal urface When body i moving under application of force P,
More informationTHE EXPERIMENTAL PERFORMANCE OF A NONLINEAR DYNAMIC VIBRATION ABSORBER
Proceeding of IMAC XXXI Conference & Expoition on Structural Dynamic February -4 Garden Grove CA USA THE EXPERIMENTAL PERFORMANCE OF A NONLINEAR DYNAMIC VIBRATION ABSORBER Yung-Sheng Hu Neil S Ferguon
More informationMechanics. Free rotational oscillations. LD Physics Leaflets P Measuring with a hand-held stop-clock. Oscillations Torsion pendulum
Mechanic Ocillation Torion pendulum LD Phyic Leaflet P.5.. Free rotational ocillation Meauring with a hand-held top-clock Object of the experiment g Meauring the amplitude of rotational ocillation a function
More information3.3. The Derivative as a Rate of Change. Instantaneous Rates of Change. DEFINITION Instantaneous Rate of Change
3.3 The Derivative a a Rate of Change 171 3.3 The Derivative a a Rate of Change In Section 2.1, we initiated the tudy of average and intantaneou rate of change. In thi ection, we continue our invetigation
More informationDiscover the answer to this question in this chapter.
Erwan, whoe ma i 65 kg, goe Bungee jumping. He ha been in free-fall for 0 m when the bungee rope begin to tretch. hat will the maximum tretching of the rope be if the rope act like a pring with a 100 N/m
More informationV = 4 3 πr3. d dt V = d ( 4 dv dt. = 4 3 π d dt r3 dv π 3r2 dv. dt = 4πr 2 dr
0.1 Related Rate In many phyical ituation we have a relationhip between multiple quantitie, and we know the rate at which one of the quantitie i changing. Oftentime we can ue thi relationhip a a convenient
More informationLinear Motion, Speed & Velocity
Add Important Linear Motion, Speed & Velocity Page: 136 Linear Motion, Speed & Velocity NGSS Standard: N/A MA Curriculum Framework (006): 1.1, 1. AP Phyic 1 Learning Objective: 3.A.1.1, 3.A.1.3 Knowledge/Undertanding
More informationControl Systems Engineering ( Chapter 7. Steady-State Errors ) Prof. Kwang-Chun Ho Tel: Fax:
Control Sytem Engineering ( Chapter 7. Steady-State Error Prof. Kwang-Chun Ho kwangho@hanung.ac.kr Tel: 0-760-453 Fax:0-760-4435 Introduction In thi leon, you will learn the following : How to find the
More informationIII.9. THE HYSTERESIS CYCLE OF FERROELECTRIC SUBSTANCES
III.9. THE HYSTERESIS CYCLE OF FERROELECTRIC SBSTANCES. Work purpoe The analyi of the behaviour of a ferroelectric ubtance placed in an eternal electric field; the dependence of the electrical polariation
More informationCHAPTER 3 LITERATURE REVIEW ON LIQUEFACTION ANALYSIS OF GROUND REINFORCEMENT SYSTEM
CHAPTER 3 LITERATURE REVIEW ON LIQUEFACTION ANALYSIS OF GROUND REINFORCEMENT SYSTEM 3.1 The Simplified Procedure for Liquefaction Evaluation The Simplified Procedure wa firt propoed by Seed and Idri (1971).
More informationAssessment Schedule 2017 Scholarship Physics (93103)
Scholarhip Phyic (93103) 201 page 1 of 5 Aement Schedule 201 Scholarhip Phyic (93103) Evidence Statement Q Evidence 1-4 mark 5-6 mark -8 mark ONE (a)(i) Due to the motion of the ource, there are compreion
More informationDisplacement vs. Distance Suppose that an object starts at rest and that the object is subject to the acceleration function t
MTH 54 Mr. Simond cla Diplacement v. Ditance Suppoe that an object tart at ret and that the object i ubject to the acceleration function t a() t = 4, t te over the time interval [,1 ]. Find both the diplacement
More informationModeling in the Frequency Domain
T W O Modeling in the Frequency Domain SOLUTIONS TO CASE STUDIES CHALLENGES Antenna Control: Tranfer Function Finding each tranfer function: Pot: V i θ i 0 π ; Pre-Amp: V p V i K; Power Amp: E a V p 50
More informationEstimating floor acceleration in nonlinear multi-story moment-resisting frames
Etimating floor acceleration in nonlinear multi-tory moment-reiting frame R. Karami Mohammadi Aitant Profeor, Civil Engineering Department, K.N.Tooi Univerity M. Mohammadi M.Sc. Student, Civil Engineering
More informationCHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS
CHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.1 INTRODUCTION 8.2 REDUCED ORDER MODEL DESIGN FOR LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.3
More informationa = f s,max /m = s g. 4. We first analyze the forces on the pig of mass m. The incline angle is.
Chapter 6 1. The greatet deceleration (of magnitude a) i provided by the maximum friction force (Eq. 6-1, with = mg in thi cae). Uing ewton econd law, we find a = f,max /m = g. Eq. -16 then give the hortet
More informationME 375 FINAL EXAM Wednesday, May 6, 2009
ME 375 FINAL EXAM Wedneday, May 6, 9 Diviion Meckl :3 / Adam :3 (circle one) Name_ Intruction () Thi i a cloed book examination, but you are allowed three ingle-ided 8.5 crib heet. A calculator i NOT allowed.
More informationHW9.2: SHM-Springs and Pendulums
HW9.: SHM-Sprin and Pendulum T S m T P Show your wor clearly on a eparate pae. Mae a etch o the problem. Start each olution with a undamental concept equation written in ymbolic ariable. Sole or the unnown
More informationELECTROMAGNETIC WAVES AND PHOTONS
CHAPTER ELECTROMAGNETIC WAVES AND PHOTONS Problem.1 Find the magnitude and direction of the induced electric field of Example.1 at r = 5.00 cm if the magnetic field change at a contant rate from 0.500
More informationPotential energy of a spring
PHYS 7: Modern Mechanic Spring 0 Homework: It i expected that a tudent work on a a homework #x hortly after lecture #x, ince HWx i on material of LECx. While the due date for HW are typically et to about
More informationHomework 7 Solution - AME 30315, Spring s 2 + 2s (s 2 + 2s + 4)(s + 20)
1 Homework 7 Solution - AME 30315, Spring 2015 Problem 1 [10/10 pt] Ue partial fraction expanion to compute x(t) when X 1 () = 4 2 + 2 + 4 Ue partial fraction expanion to compute x(t) when X 2 () = ( )
More informationME 141. Engineering Mechanics
ME 141 Engineering Mechanic Lecture 14: Plane motion of rigid bodie: Force and acceleration Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: hakil@me.buet.ac.bd, hakil6791@gmail.com
More information3pt3pt 3pt3pt0pt 1.5pt3pt3pt Honors Physics Impulse-Momentum Theorem. Name: Answer Key Mr. Leonard
3pt3pt 3pt3pt0pt 1.5pt3pt3pt Honor Phyic Impule-Momentum Theorem Spring, 2017 Intruction: Complete the following workheet. Show all of you work. Name: Anwer Key Mr. Leonard 1. A 0.500 kg ball i dropped
More informationSimulation Study on the Shock Properties of the Double-Degree-of-Freedom Cushioning Packaging System
Proceeding of the 7th IAPRI World Conference on Packaging Simulation Study on the Shock Propertie of the Double-Degree-of-Freedom Cuhioning Packaging Sytem Xia Zhu, Qiaoqiao Yan, Xiaoling Yao, Junbin Chen,
More informationEP225 Note No. 5 Mechanical Waves
EP5 Note No. 5 Mechanical Wave 5. Introduction Cacade connection of many ma-pring unit conitute a medium for mechanical wave which require that medium tore both kinetic energy aociated with inertia (ma)
More informationModule: 8 Lecture: 1
Moule: 8 Lecture: 1 Energy iipate by amping Uually amping i preent in all ocillatory ytem. It effect i to remove energy from the ytem. Energy in a vibrating ytem i either iipate into heat oun or raiate
More informationTarzan s Dilemma for Elliptic and Cycloidal Motion
Tarzan Dilemma or Elliptic and Cycloidal Motion Yuji Kajiyama National Intitute o Technology, Yuge College, Shimo-Yuge 000, Yuge, Kamijima, Ehime, 794-593, Japan kajiyama@gen.yuge.ac.jp btract-in thi paper,
More informationHalliday/Resnick/Walker 7e Chapter 6
HRW 7e Chapter 6 Page of Halliday/Renick/Walker 7e Chapter 6 3. We do not conider the poibility that the bureau might tip, and treat thi a a purely horizontal motion problem (with the peron puh F in the
More informationMidterm Review - Part 1
Honor Phyic Fall, 2016 Midterm Review - Part 1 Name: Mr. Leonard Intruction: Complete the following workheet. SHOW ALL OF YOUR WORK. 1. Determine whether each tatement i True or Fale. If the tatement i
More informationSKAA 1213 Engineering Mechanics
SKAA 113 Engineering Mechanic TOPIC 8 KINEMATIC OF PARTICLES Lecturer: Roli Anang Dr. Mohd Yunu Ihak Dr. Tan Cher Siang Outline Introduction Rectilinear Motion Curilinear Motion Problem Introduction General
More informationSolving Differential Equations by the Laplace Transform and by Numerical Methods
36CH_PHCalter_TechMath_95099 3//007 :8 PM Page Solving Differential Equation by the Laplace Tranform and by Numerical Method OBJECTIVES When you have completed thi chapter, you hould be able to: Find the
More informationBasics of a Quartz Crystal Microbalance
Baic of a Quartz Crytal Microbalance Introduction Thi document provide an introduction to the quartz crytal microbalance (QCM) which i an intrument that allow a uer to monitor mall ma change on an electrode.
More informationMAE 101A. Homework 3 Solutions 2/5/2018
MAE 101A Homework 3 Solution /5/018 Munon 3.6: What preure gradient along the treamline, /d, i required to accelerate water upward in a vertical pipe at a rate of 30 ft/? What i the anwer if the flow i
More informationPHYS 110B - HW #2 Spring 2004, Solutions by David Pace Any referenced equations are from Griffiths Problem statements are paraphrased
PHYS 11B - HW # Spring 4, Solution by David Pace Any referenced equation are from Griffith Problem tatement are paraphraed [1.] Problem 7. from Griffith A capacitor capacitance, C i charged to potential
More informationNCAAPMT Calculus Challenge Challenge #3 Due: October 26, 2011
NCAAPMT Calculu Challenge 011 01 Challenge #3 Due: October 6, 011 A Model of Traffic Flow Everyone ha at ome time been on a multi-lane highway and encountered road contruction that required the traffic
More information( kg) (410 m/s) 0 m/s J. W mv mv m v v. 4 mv
PHYS : Solution to Chapter 6 Home ork. RASONING a. The work done by the gravitational orce i given by quation 6. a = (F co θ). The gravitational orce point downward, oppoite to the upward vertical diplacement
More informationCorrection for Simple System Example and Notes on Laplace Transforms / Deviation Variables ECHE 550 Fall 2002
Correction for Simple Sytem Example and Note on Laplace Tranform / Deviation Variable ECHE 55 Fall 22 Conider a tank draining from an initial height of h o at time t =. With no flow into the tank (F in
More informationLecture Notes II. As the reactor is well-mixed, the outlet stream concentration and temperature are identical with those in the tank.
Lecture Note II Example 6 Continuou Stirred-Tank Reactor (CSTR) Chemical reactor together with ma tranfer procee contitute an important part of chemical technologie. From a control point of view, reactor
More informationCHAPTER 4 DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL
98 CHAPTER DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL INTRODUCTION The deign of ytem uing tate pace model for the deign i called a modern control deign and it i
More informationSupplementary Figures
Supplementary Figure Supplementary Figure S1: Extraction of the SOF. The tandard deviation of meaured V xy at aturated tate (between 2.4 ka/m and 12 ka/m), V 2 d Vxy( H, j, hm ) Vxy( H, j, hm ) 2. The
More informationPhysics Exam 3 Formulas
Phyic 10411 Exam III November 20, 2009 INSTRUCTIONS: Write your NAME on the front of the blue exam booklet. The exam i cloed book, and you may have only pen/pencil and a calculator (no tored equation or
More informationCumulative Review of Calculus
Cumulative Review of Calculu. Uing the limit definition of the lope of a tangent, determine the lope of the tangent to each curve at the given point. a. f 5,, 5 f,, f, f 5,,,. The poition, in metre, of
More informationChapter 5 Consistency, Zero Stability, and the Dahlquist Equivalence Theorem
Chapter 5 Conitency, Zero Stability, and the Dahlquit Equivalence Theorem In Chapter 2 we dicued convergence of numerical method and gave an experimental method for finding the rate of convergence (aka,
More informationGreen-Kubo formulas with symmetrized correlation functions for quantum systems in steady states: the shear viscosity of a fluid in a steady shear flow
Green-Kubo formula with ymmetrized correlation function for quantum ytem in teady tate: the hear vicoity of a fluid in a teady hear flow Hirohi Matuoa Department of Phyic, Illinoi State Univerity, Normal,
More informationConstant Force: Projectile Motion
Contant Force: Projectile Motion Abtract In thi lab, you will launch an object with a pecific initial velocity (magnitude and direction) and determine the angle at which the range i a maximum. Other tak,
More informationModule 4: Time Response of discrete time systems Lecture Note 1
Digital Control Module 4 Lecture Module 4: ime Repone of dicrete time ytem Lecture Note ime Repone of dicrete time ytem Abolute tability i a baic requirement of all control ytem. Apart from that, good
More informationLecture 15 - Current. A Puzzle... Advanced Section: Image Charge for Spheres. Image Charge for a Grounded Spherical Shell
Lecture 15 - Current Puzzle... Suppoe an infinite grounded conducting plane lie at z = 0. charge q i located at a height h above the conducting plane. Show in three different way that the potential below
More informationSecond Law of Motion. Force mass. Increasing mass. (Neglect air resistance in this example)
Newton Law of Motion Moentu and Energy Chapter -3 Second Law of Motion The acceleration of an object i directly proportional to the net force acting on the object, i in the direction of the net force,
More informationSocial Studies 201 Notes for March 18, 2005
1 Social Studie 201 Note for March 18, 2005 Etimation of a mean, mall ample ize Section 8.4, p. 501. When a reearcher ha only a mall ample ize available, the central limit theorem doe not apply to the
More informationTechnical Appendix: Auxiliary Results and Proofs
A Technical Appendix: Auxiliary Reult and Proof Lemma A. The following propertie hold for q (j) = F r [c + ( ( )) ] de- ned in Lemma. (i) q (j) >, 8 (; ]; (ii) R q (j)d = ( ) q (j) + R q (j)d ; (iii) R
More informationPulsed Magnet Crimping
Puled Magnet Crimping Fred Niell 4/5/00 1 Magnetic Crimping Magnetoforming i a metal fabrication technique that ha been in ue for everal decade. A large capacitor bank i ued to tore energy that i ued to
More informationFinal Comprehensive Exam Physical Mechanics Friday December 15, Total 100 Points Time to complete the test: 120 minutes
Final Comprehenive Exam Phyical Mechanic Friday December 15, 000 Total 100 Point Time to complete the tet: 10 minute Pleae Read the Quetion Carefully and Be Sure to Anwer All Part! In cae that you have
More informationEE C128 / ME C134 Problem Set 1 Solution (Fall 2010) Wenjie Chen and Jansen Sheng, UC Berkeley
EE C28 / ME C34 Problem Set Solution (Fall 200) Wenjie Chen and Janen Sheng, UC Berkeley. (0 pt) BIBO tability The ytem h(t) = co(t)u(t) i not BIBO table. What i the region of convergence for H()? A bounded
More informationUniform Acceleration Problems Chapter 2: Linear Motion
Name Date Period Uniform Acceleration Problem Chapter 2: Linear Motion INSTRUCTIONS: For thi homework, you will be drawing a coordinate axi (in math lingo: an x-y board ) to olve kinematic (motion) problem.
More informationOnline supplementary information
Electronic Supplementary Material (ESI) for Soft Matter. Thi journal i The Royal Society of Chemitry 15 Online upplementary information Governing Equation For the vicou flow, we aume that the liquid thickne
More informationFluid-structure coupling analysis and simulation of viscosity effect. on Coriolis mass flowmeter
APCOM & ISCM 11-14 th December, 2013, Singapore luid-tructure coupling analyi and imulation of vicoity effect on Corioli ma flowmeter *Luo Rongmo, and Wu Jian National Metrology Centre, A*STAR, 1 Science
More informationECE-320 Linear Control Systems. Spring 2014, Exam 1. No calculators or computers allowed, you may leave your answers as fractions.
ECE-0 Linear Control Sytem Spring 04, Exam No calculator or computer allowed, you may leave your anwer a fraction. All problem are worth point unle noted otherwie. Total /00 Problem - refer to the unit
More informationThe Multilayer Impedance Pump Model
12 Chapter 2 The Multilayer Impedance Pump Model 2.1 Phyical model The MIP wa a luid-illed elatic tube with an excitation zone located aymmetrically with repect to the length o the pump. The pump had an
More information7.2 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 281
72 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 28 and i 2 Show how Euler formula (page 33) can then be ued to deduce the reult a ( a) 2 b 2 {e at co bt} {e at in bt} b ( a) 2 b 2 5 Under what condition
More informationCake ltration analysis the eect of the relationship between the pore liquid pressure and the cake compressive stress
Chemical Engineering Science 56 (21) 5361 5369 www.elevier.com/locate/ce Cake ltration analyi the eect of the relationhip between the pore liquid preure and the cake compreive tre C. Tien, S. K. Teoh,
More informationPhysics 111. Exam #3. March 4, 2011
Phyic Exam #3 March 4, 20 Name Multiple Choice /6 Problem # /2 Problem #2 /2 Problem #3 /2 Problem #4 /2 Total /00 PartI:Multiple Choice:Circlethebetanwertoeachquetion.Anyothermark willnotbegivencredit.eachmultiple
More informationHomework 12 Solution - AME30315, Spring 2013
Homework 2 Solution - AME335, Spring 23 Problem :[2 pt] The Aerotech AGS 5 i a linear motor driven XY poitioning ytem (ee attached product heet). A friend of mine, through careful experimentation, identified
More informationPhysics 218: Exam 1. Class of 2:20pm. February 14th, You have the full class period to complete the exam.
Phyic 218: Exam 1 Cla of 2:20pm February 14th, 2012. Rule of the exam: 1. You have the full cla period to complete the exam. 2. Formulae are provided on the lat page. You may NOT ue any other formula heet.
More informationPosition. If the particle is at point (x, y, z) on the curved path s shown in Fig a,then its location is defined by the position vector
34 C HAPTER 1 KINEMATICS OF A PARTICLE 1 1.5 Curvilinear Motion: Rectangular Component Occaionall the motion of a particle can bet be decribed along a path that can be epreed in term of it,, coordinate.
More informationConservation of Energy
Conervative Force Conervation of Energ force i conervative if the work done b the force from r to r, but depend on initial and final poition onl Conervative Non-conervative Section #4.5 #4.6 Conervation
More informationThe Hassenpflug Matrix Tensor Notation
The Haenpflug Matrix Tenor Notation D.N.J. El Dept of Mech Mechatron Eng Univ of Stellenboch, South Africa e-mail: dnjel@un.ac.za 2009/09/01 Abtract Thi i a ample document to illutrate the typeetting of
More information2015 PhysicsBowl Solutions Ans Ans Ans Ans Ans B 2. C METHOD #1: METHOD #2: 3. A 4.
05 PhyicBowl Solution # An # An # An # An # An B B B 3 D 4 A C D A 3 D 4 C 3 A 3 C 3 A 33 C 43 B 4 B 4 D 4 C 34 A 44 E 5 E 5 E 5 E 35 E 45 B 6 D 6 A 6 A 36 B 46 E 7 A 7 D 7 D 37 A 47 C 8 E 8 C 8 B 38 D
More informationThe Electric Potential Energy
Lecture 6 Chapter 28 Phyic II The Electric Potential Energy Coure webite: http://aculty.uml.edu/andriy_danylov/teaching/phyicii New Idea So ar, we ued vector quantitie: 1. Electric Force (F) Depreed! 2.
More informationPHYSICS 211 MIDTERM II 12 May 2004
PHYSIS IDTER II ay 004 Exa i cloed boo, cloed note. Ue only your forula heet. Write all wor and anwer in exa boolet. The bac of page will not be graded unle you o requet on the front of the page. Show
More informationFermi Distribution Function. n(e) T = 0 T > 0 E F
LECTURE 3 Maxwell{Boltzmann, Fermi, and Boe Statitic Suppoe we have a ga of N identical point particle in a box ofvolume V. When we ay \ga", we mean that the particle are not interacting with one another.
More informationA FUNCTIONAL BAYESIAN METHOD FOR THE SOLUTION OF INVERSE PROBLEMS WITH SPATIO-TEMPORAL PARAMETERS AUTHORS: CORRESPONDENCE: ABSTRACT
A FUNCTIONAL BAYESIAN METHOD FOR THE SOLUTION OF INVERSE PROBLEMS WITH SPATIO-TEMPORAL PARAMETERS AUTHORS: Zenon Medina-Cetina International Centre for Geohazard / Norwegian Geotechnical Intitute Roger
More informationB (x) 0. Region 1. v x. Region 2 NNSS 0.5. abs(an + i Bn) [T] n NSNS 0.5. abs(an + i Bn) [T] n
Analytical Calculation of Field Force and Loe of a Radial Magnetic Bearing With a Rotating Rotor Conidering Eddy Current Marku Ahren International Center for Magnetic Bearing ETH urich Switzerland Ladilav
More informationName: Answer Key Date: Regents Physics. Energy
Nae: Anwer Key Date: Regent Phyic Tet # 9 Review Energy 1. Ue GUESS ethod and indicate all vector direction.. Ter to know: work, power, energy, conervation of energy, work-energy theore, elatic potential
More informationChapter 7. Root Locus Analysis
Chapter 7 Root Locu Analyi jw + KGH ( ) GH ( ) - K 0 z O 4 p 2 p 3 p Root Locu Analyi The root of the cloed-loop characteritic equation define the ytem characteritic repone. Their location in the complex
More information1. A 500-kilogram car is driving at 15 meters/second. What's its kinetic energy? How much does the car weigh?
9. Solution Work & Energy Homework - KINETIC ENERGY. A 500-kilogram car i driing at 5 meter/econd. What' it kinetic energy? How much doe the car weigh? m= 500 kg 5 m/ Write Equation: Kinetic Energy = ½
More informationPOSTER PRESENTATION OF A PAPER BY: Alex Shved, Mark Logillo, Spencer Studley AAPT MEETING, JANUARY, 2002, PHILADELPHIA
POSTER PRESETATIO OF A PAPER BY: Ale Shved, Mar Logillo, Spencer Studley AAPT MEETIG, JAUARY, 00, PHILADELPHIA Daped Haronic Ocillation Uing Air a Drag Force Spencer Studley Ale Shveyd Mar Loguillo Santa
More informationUNITS FOR THERMOMECHANICS
UNITS FOR THERMOMECHANICS 1. Conitent Unit. Every calculation require a conitent et of unit. Hitorically, one et of unit wa ued for mechanic and an apparently unrelated et of unit wa ued for heat. For
More informationLateral vibration of footbridges under crowd-loading: Continuous crowd modeling approach
ateral vibration of footbridge under crowd-loading: Continuou crowd modeling approach Joanna Bodgi, a, Silvano Erlicher,b and Pierre Argoul,c Intitut NAVIER, ENPC, 6 et 8 av. B. Pacal, Cité Decarte, Champ
More informationonline learning Unit Workbook 4 RLC Transients
online learning Pearon BTC Higher National in lectrical and lectronic ngineering (QCF) Unit 5: lectrical & lectronic Principle Unit Workbook 4 in a erie of 4 for thi unit Learning Outcome: RLC Tranient
More informationElastic Collisions Definition Examples Work and Energy Definition of work Examples. Physics 201: Lecture 10, Pg 1
Phyic 131: Lecture Today Agenda Elatic Colliion Definition i i Example Work and Energy Definition of work Example Phyic 201: Lecture 10, Pg 1 Elatic Colliion During an inelatic colliion of two object,
More informationSolving Radical Equations
10. Solving Radical Equation Eential Quetion How can you olve an equation that contain quare root? Analyzing a Free-Falling Object MODELING WITH MATHEMATICS To be proficient in math, you need to routinely
More informationAn analysis of the self-excited torsional vibrations of the electromechanical drive system
Vibration in Phyical Sytem Vol. 7 (16) An analyi of the elf-excited torional vibration of the electromechanical drive ytem Robert KONOWROCKI and Tomaz SZOLC Intitute of Fundamental Technological Reearch
More information3.7 Spring Systems 253
3.7 Spring Systems 253 The resulting amplification of vibration eventually becomes large enough to destroy the mechanical system. This is a manifestation of resonance discussed further in Section??. Exercises
More informationCONFERENCE PROCEEDINGS VOLUME I
FILTECH 005 CONFERENCE PROCEEDINGS VOLUME I Conference Date: October -3, 005 Venue: Organizer: Rhein-Main-Hallen Rheintr. 0 6508 Wiebaden Germany Filtech Exhibition Germany PO Box 5 40637 Meerbuch Germany
More informationAP Physics Charge Wrap up
AP Phyic Charge Wrap up Quite a few complicated euation for you to play with in thi unit. Here them babie i: F 1 4 0 1 r Thi i good old Coulomb law. You ue it to calculate the force exerted 1 by two charge
More informationMath 273 Solutions to Review Problems for Exam 1
Math 7 Solution to Review Problem for Exam True or Fale? Circle ONE anwer for each Hint: For effective tudy, explain why if true and give a counterexample if fale (a) T or F : If a b and b c, then a c
More informationSample Problems. Lecture Notes Related Rates page 1
Lecture Note Related Rate page 1 Sample Problem 1. A city i of a circular hape. The area of the city i growing at a contant rate of mi y year). How fat i the radiu growing when it i exactly 15 mi? (quare
More informationOnline Appendix for Managerial Attention and Worker Performance by Marina Halac and Andrea Prat
Online Appendix for Managerial Attention and Worker Performance by Marina Halac and Andrea Prat Thi Online Appendix contain the proof of our reult for the undicounted limit dicued in Section 2 of the paper,
More informationAn Interesting Property of Hyperbolic Paraboloids
Page v w Conider the generic hyperbolic paraboloid defined by the equation. u = where a and b are aumed a b poitive. For our purpoe u, v and w are a permutation of x, y, and z. A typical graph of uch a
More informationMidterm Test Nov 10, 2010 Student Number:
Mathematic 265 Section: 03 Verion A Full Name: Midterm Tet Nov 0, 200 Student Number: Intruction: There are 6 page in thi tet (including thi cover page).. Caution: There may (or may not) be more than one
More informationUnit 2 Linear Motion
Unit Linear Motion Linear Motion Key Term - How to calculate Speed & Ditance 1) Motion Term: a. Symbol for time = (t) b. Diplacement (X) How far omething travel in a given direction. c. Rate How much omething
More informationQuantifying And Specifying The Dynamic Response Of Flowmeters
White Paper Quantifying And Specifying The Dynamic Repone Of Flowmeter DP Flow ABSTRACT The dynamic repone characteritic of flowmeter are often incompletely or incorrectly pecified. Thi i often the reult
More informationMODELLING OF FRICTIONAL SOIL DAMPING IN FINITE ELEMENT ANALYSIS
MODELLING OF FRICTIONAL SOIL DAMPING IN FINITE ELEMENT ANALYSIS S. VAN BAARS Department of Science, Technology and Communication, Univerity of Luxembourg, Luxembourg ABSTRACT: In oil dynamic, the oil i
More informationPhysics 20 Lesson 28 Simple Harmonic Motion Dynamics & Energy
Phyic 0 Leon 8 Siple Haronic Motion Dynaic & Energy Now that we hae learned about work and the Law of Coneration of Energy, we are able to look at how thee can be applied to the ae phenoena. In general,
More informationBernoulli s equation may be developed as a special form of the momentum or energy equation.
BERNOULLI S EQUATION Bernoulli equation may be developed a a pecial form of the momentum or energy equation. Here, we will develop it a pecial cae of momentum equation. Conider a teady incompreible flow
More informationState Space: Observer Design Lecture 11
State Space: Oberver Deign Lecture Advanced Control Sytem Dr Eyad Radwan Dr Eyad Radwan/ACS/ State Space-L Controller deign relie upon acce to the tate variable for feedback through adjutable gain. Thi
More information18.03SC Final Exam = x 2 y ( ) + x This problem concerns the differential equation. dy 2
803SC Final Exam Thi problem concern the differential equation dy = x y ( ) dx Let y = f (x) be the olution with f ( ) = 0 (a) Sketch the iocline for lope, 0, and, and ketch the direction field along them
More informationBogoliubov Transformation in Classical Mechanics
Bogoliubov Tranformation in Claical Mechanic Canonical Tranformation Suppoe we have a et of complex canonical variable, {a j }, and would like to conider another et of variable, {b }, b b ({a j }). How
More information