Mechanical System. Seoul National Univ. School of Mechanical and Aerospace Engineering. Spring 2008
|
|
- Bryce Copeland
- 5 years ago
- Views:
Transcription
1 Mechanical Syste
2 Newton s Laws 1)First law : conservation of oentu no external force no oentu change linear oentu : v Jω angular oentu : dv ) Second law : F = a= dt d T T = J α = J ω dt
3 Three Basic Eleents in Modeling Mechanical Systes i) Inertial eleents ( kinetic energy ): asses: M oents of inertial : J ii) Spring eleents ( Potential energy ) T = k Δθ = k( θ ) 1 θ θ ΔX Torsional spring iii) Daper eleents ( energy dissipation ) Δθ T ΔX b θ θ F = bx T θ T = b θ θ b x x x
4 Exaples of Modeling Mechanical Systes t =, ω() = ω ex1) equation of otion : bw J b dω J = b ω dt dω dω b J + bω = + ω = dt dt J λt λt b λt let, ω( t) = ce λe + e = J b λ = J b t J ω() t = ce, t =, ω() = ω = C ω() t = ω e o b t J ω 1 e =.368ω ω() t w
5 Exaples of Modeling Mechanical Systes ex) Spring-Mass x(t) k t =, x() = x, x() = d x = F = kx dt k x && + kx = && x + x = k k xt () = Acos t+ Bsin t x () = A = x o k k k k k x& () = A sin t + B cos t = B = k xt () = x cos t = x cos ω n t π Period T = [sec] k/ 1 1 k Frequency f = = [ Hz] T π Natural frequency k ωn = π f = [ rad /sec]
6 Exaples of Modeling Mechanical Systes Spring-ass-daper x() x& () = = x x& d x = kx bx& dt b k && x + x& x + = k b b let, = ωn, = ζωn, = ζ k && + & + λ + ζωλ + ωx ω = x+ ζω + =, () = λt nx ωnx xt c e n n x ( ) λ = ζω ± ζω ω = ζω ± ζ 1ω n n n n n
7 Exaples of Modeling Mechanical Systes b k && x + x & x + = x() = x x& () = x& = k b b k let, = ωn, = ζωn, = ζ && x+ x& + x= Laplace Transfor ζω n ω n ( sxs ( ) sx x& ) + ζω ( sxs ( ) x ) + ω Xs ( ) = n n ( s + ζωns+ ωn) X( s) s x ζωnx = ( s + ζω n s+ ω n) X ( s ) = s x + ζω nx X() s = s x + ζω x s n + ζωns+ ωn
8 Exaples of Modeling Mechanical Systes s x + ζω x s x ζω x n n () = = + s + ζωns+ ωn s + ζωns+ ωn s + ζωns+ ωn X s s s + ζω s+ ω : charateristic polynoial n n + ζω s + ω = : characteistic i equation n n ( ) n n n n n s = ζω ± ζω ω = ζω ± ω ζ 1 : charateristic roots 1) ζ < 1 underdaped s = ζω ± ω ζ 1= ζω ± jω 1 ζ n n n n ( s+ ζω ) x ζω x X() s = + ( s+ ζω ) + ω (1 ζ ) ( + ζω ) + ω (1 ζ ) n n n n s n n ζω ζ n xt () = e t xcos 1 ζ ωnt+ x sin ζ ωnt 1 ζ
9 Exaples of Modeling Mechanical Systes ) ζ > 1 overdaped s = ζωn ± ωn ζ X() s = 1 ( s+ ζω ) x ( s + ζω 1)( 1) n ωn ζ s+ ζωn + ωn ζ ( ζωn+ ζ 1 ωn) t ( ζωn ζ 1 ωn) xt () = ke + ke 1 n t 3) ζ = 1 critically daped s = ζωn ( s+ ζωn) x X() s = s + ζω ( ) ( ζω ) t ( ζω ) xt ke kte n n () = + n 1 t
10 Exaples of Modeling Mechanical Systes 1) ζ < 1 Underdaped ζω ζ n x() t = e t xcos 1 ζ ωnt+ x sin ζ ωnt 1 ζ ω n : ζ : natural frequency daping ratio ω d = 1 ζ ωn ) ζ > 1 Overdaped ( ζωn+ ζ 1 ωn) t ( ζωn ζ 1 ωn) xt () = ke + ke 1 λ = ζωn ± ζ 1ω n t x () t ζ > 1 ζ = 1 3) ζ = 1 λ = ζωn xt ke kte n ζωn () = + ζω t 1 t ζ < 1 t
11 Dry Friction (no lubricant) Fμs = Static Friction Force Fμk = Kinetic Friction Force Fμs = μs N μs : Static Friction Coefficient Fμk = μk N k N μk k : Kinetic Friction Coefficient x & = x F μ F if F F = F μssgn( F) if F> F μs μs & F = F sgn( x& ) μ μk
12 ε Friction (with lubricant) bx& + G N sgn( x& ) x& > ε F & μ = F if x < ε and F ( Fs + G N) ( F + s G N)sgn( F) otherwise i.e., if x& < ε and F > ( F + s G N) b: viscous friction coefficient G: load-dependent factor N: noral force Fs: the axiu static friction ε : a sall bound for zero velocity detection
13 Work, Energy, and Power Mechanical work : W = F x [N ] = [Joule] = Force displaceent Energy : capacity or ability to do work. Electrical, Cheical, Mechanical, etc. Mechanical energy : Potential energy position Kinetic energy velocity
14 Potential Energy ex1) F = kx x1 x1 1 dw = Fdx = kx dx dw = kx dx = kx ex) M Mg E h 1 X= = gx (Potential Energy)
15 Kinetic Energy 1 v v : J ω : 1 Jω
16 Work and Energy Syste + External Work = E Energy E1 W E 1 + W = E F v1 v1 l v v E1+ W = E 1 1 v 1 + Fl= v 1 1 v 1 Fl= v
17 Power Power : tie rate & doing work P dw N = dt = sec [ Watt ] Ex) kg V = 7k/h = /s (in 1sec) V = 1 1 v + W = v 1 ()() [ ] W = = N = kn kj W 4 1 N P = = t 1 sec = 4 1 N / s = 4 1 W = 4W 1 hp = W P = 54 hp Power dissipated in a daper P = Fv = bx& x& = bx&
18 An Energy Method for Deriving Equations of Motion Conservative syste : No energy dissipation E + W = E 1 E E = W 1 Kinetic Energy T Potential Energy U Δ(T+U) = ΔW (the change in the total energy) = (the net work done on the syste by the external force) no external force ; ΔW = Δ(T+U) = T+U = constant
19 Exaples of Energy Method x(t) ex1) 1 1 T = x&, U = kx, T + U = C k 1 1 x& + kx = d ( T + U ) =, xx &&& + kxx & = ( x && + kx ) x & = dt x&, ( x && + kx ) = 1 1 d ( T + U ) = bx &, xx &&& + kxx & = bxx && = dt ( x && + kx + bx& ) x& = ex) x(t) x T = x&, U = kx k x&, ( x && + kx+ bx& ) =
20 ex3) Exaples of Energy Method Spring with ass ξ l + x x dξ s l + x k l Potential E x(t) 1 U = kx x+ kx ω n = = k 1 dξ ξ dt = s ( x& ) l + x l + x l+ x l+ x = 1 1 dt s + x& ξ l x d ξ 3 ( ) = x s & ( 3 l + x ) ( l+ x) Kinetic E 1 T = x 1 1 = ( 3 s ) x& T = x& + ( s ) x& = ( + s ) x& ( + s )& x + kx = ω n = k s
Chapter 2: Introduction to Damping in Free and Forced Vibrations
Chapter 2: Introduction to Daping in Free and Forced Vibrations This chapter ainly deals with the effect of daping in two conditions like free and forced excitation of echanical systes. Daping plays an
More informationDynamics of structures
Dynamics of structures 1.2 Viscous damping Luc St-Pierre October 30, 2017 1 / 22 Summary so far We analysed the spring-mass system and found that its motion is governed by: mẍ(t) + kx(t) = 0 k y m x x
More informationSimple Harmonic Motion
Reading: Chapter 15 Siple Haronic Motion Siple Haronic Motion Frequency f Period T T 1. f Siple haronic otion x ( t) x cos( t ). Aplitude x Phase Angular frequency Since the otion returns to its initial
More informationwhich proves the motion is simple harmonic. Now A = a 2 + b 2 = =
Worked out Exaples. The potential energy function for the force between two atos in a diatoic olecules can be expressed as follows: a U(x) = b x / x6 where a and b are positive constants and x is the distance
More informationDefinition of Work, The basics
Physics 07 Lecture 16 Lecture 16 Chapter 11 (Work) v Eploy conservative and non-conservative forces v Relate force to potential energy v Use the concept of power (i.e., energy per tie) Chapter 1 v Define
More informationCHECKLIST. r r. Newton s Second Law. natural frequency ω o (rad.s -1 ) (Eq ) a03/p1/waves/waves doc 9:19 AM 29/03/05 1
PHYS12 Physics 1 FUNDAMENTALS Module 3 OSCILLATIONS & WAVES Text Physics by Hecht Chapter 1 OSCILLATIONS Sections: 1.5 1.6 Exaples: 1.6 1.7 1.8 1.9 CHECKLIST Haronic otion, periodic otion, siple haronic
More informationSIMPLE HARMONIC MOTION: NEWTON S LAW
SIMPLE HARMONIC MOTION: NEWTON S LAW siple not siple PRIOR READING: Main 1.1, 2.1 Taylor 5.1, 5.2 http://www.yoops.org/twocw/it/nr/rdonlyres/physics/8-012fall-2005/7cce46ac-405d-4652-a724-64f831e70388/0/chp_physi_pndul.jpg
More informationWork, Energy and Momentum
Work, Energy and Moentu Work: When a body oves a distance d along straight line, while acted on by a constant force of agnitude F in the sae direction as the otion, the work done by the force is tered
More informationMathematical Modeling and response analysis of mechanical systems are the subjects of this chapter.
Chapter 3 Mechanical Systems A. Bazoune 3.1 INRODUCION Mathematical Modeling and response analysis of mechanical systems are the subjects of this chapter. 3. MECHANICAL ELEMENS Any mechanical system consists
More informationPhysics 41 HW Set 1 Chapter 15 Serway 7 th Edition
Physics HW Set Chapter 5 Serway 7 th Edition Conceptual Questions:, 3, 5,, 6, 9 Q53 You can take φ = π, or equally well, φ = π At t= 0, the particle is at its turning point on the negative side of equilibriu,
More informationPHYSICS 110A : CLASSICAL MECHANICS MIDTERM EXAM #2
PHYSICS 110A : CLASSICAL MECHANICS MIDTERM EXAM #2 [1] Two blocks connected by a spring of spring constant k are free to slide frictionlessly along a horizontal surface, as shown in Fig. 1. The unstretched
More informationFOUNDATION STUDIES EXAMINATIONS January 2016
1 FOUNDATION STUDIES EXAMINATIONS January 2016 PHYSICS Seester 2 Exa July Fast Track Tie allowed 2 hours for writing 10 inutes for reading This paper consists of 4 questions printed on 11 pages. PLEASE
More informationPeriodic Motion is everywhere
Lecture 19 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand and use energy conservation
More informationLecture #8-3 Oscillations, Simple Harmonic Motion
Lecture #8-3 Oscillations Siple Haronic Motion So far we have considered two basic types of otion: translation and rotation. But these are not the only two types of otion we can observe in every day life.
More informationWork and Kinetic Energy
Chapter 6 Work and Kinetic Energy PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Copyright 2008 Pearson Education Inc., publishing
More informationPhysics 2210 Fall smartphysics 20 Conservation of Angular Momentum 21 Simple Harmonic Motion 11/23/2015
Physics 2210 Fall 2015 sartphysics 20 Conservation of Angular Moentu 21 Siple Haronic Motion 11/23/2015 Exa 4: sartphysics units 14-20 Midter Exa 2: Day: Fri Dec. 04, 2015 Tie: regular class tie Section
More information1 (40) Gravitational Systems Two heavy spherical (radius 0.05R) objects are located at fixed positions along
(40) Gravitational Systes Two heavy spherical (radius 0.05) objects are located at fixed positions along 2M 2M 0 an axis in space. The first ass is centered at r = 0 and has a ass of 2M. The second ass
More informationChapter 2 SDOF Vibration Control 2.1 Transfer Function
Chapter SDOF Vibration Control.1 Transfer Function mx ɺɺ( t) + cxɺ ( t) + kx( t) = F( t) Defines the transfer function as output over input X ( s) 1 = G( s) = (1.39) F( s) ms + cs + k s is a complex number:
More informationT m. Fapplied. Thur Oct 29. ω = 2πf f = (ω/2π) T = 1/f. k m. ω =
Thur Oct 9 Assignent 10 Mass-Spring Kineatics (x, v, a, t) Dynaics (F,, a) Tie dependence Energy Pendulu Daping and Resonances x Acos( ωt) = v = Aω sin( ωt) a = Aω cos( ωt) ω = spring k f spring = 1 k
More information0J2 - Mechanics Lecture Notes 2
0J2 - Mechanics Lecture Notes 2 Work, Power, Energy Work If a force is applied to a body, which then moves, we say the force does work. In 1D, if the force is constant with magnitude F, and the body moves
More informationDRAFT. Memo. Contents. To whom it may concern SVN: Jan Mooiman +31 (0) nl
Meo To To who it ay concern Date Reference Nuber of pages 219-1-16 SVN: 5744 22 Fro Direct line E-ail Jan Mooian +31 )88 335 8568 jan.ooian@deltares nl +31 6 4691 4571 Subject PID controller ass-spring-daper
More informationPhysics 2101 S c e t c i cti n o 3 n 3 March 31st Announcements: Quiz today about Ch. 14 Class Website:
Physics 2101 Section 3 March 31 st Announcements: Quiz today about Ch. 14 Class Website: http://www.phys.lsu.edu/classes/spring2010/phys2101 3/ http://www.phys.lsu.edu/~jzhang/teaching.html Simple Harmonic
More informationand ζ in 1.1)? 1.2 What is the value of the magnification factor M for system A, (with force frequency ω = ωn
EN40: Dynais and Vibrations Hoework 6: Fored Vibrations, Rigid Body Kineatis Due Friday April 7, 017 Shool of Engineering Brown University 1. Syste A in the figure is ritially daped. The aplitude of the
More information+ 1 2 mv 2. Since no forces act on the system in the x-direction, linear momentum in x-direction is conserved: (2) 0 = mv A2. + Rω 2.
ME 74 Spring 018 Final Exaination Proble 1 Given: hoogeneous dis of ass and outer radius R is able to roll without slipping on the curved upper surface of a cart. art (of ass ) is able to ove along a sooth,
More informationVTU-NPTEL-NMEICT Project
MODULE-II --- SINGLE DOF FREE S VTU-NPTEL-NMEICT Project Progress Report The Project on Development of Remaining Three Quadrants to NPTEL Phase-I under grant in aid NMEICT, MHRD, New Delhi SME Name : Course
More informationChapter 5 Oscillatory Motion
Chapter 5 Oscillatory Motion Simple Harmonic Motion An object moves with simple harmonic motion whenever its acceleration is proportional to its displacement from some equilibrium position and is oppositely
More informationExam 2 Spring 2014
95.141 Exam 2 Spring 2014 Section number Section instructor Last/First name Last 3 Digits of Student ID Number: Answer all questions, beginning each new question in the space provided. Show all work. Show
More informationIn the session you will be divided into groups and perform four separate experiments:
Mechanics Lab (Civil Engineers) Nae (please print): Tutor (please print): Lab group: Date of lab: Experients In the session you will be divided into groups and perfor four separate experients: (1) air-track
More informationVibrations: Two Degrees of Freedom Systems - Wilberforce Pendulum and Bode Plots
.003J/.053J Dynaics and Control, Spring 007 Professor Peacock 5/4/007 Lecture 3 Vibrations: Two Degrees of Freedo Systes - Wilberforce Pendulu and Bode Plots Wilberforce Pendulu Figure : Wilberforce Pendulu.
More informationClassical Mechanics Small Oscillations
Classical Mechanics Sall Oscillations Dipan Kuar Ghosh UM-DAE Centre for Excellence in Basic Sciences, Kalina Mubai 400098 Septeber 4, 06 Introduction When a conservative syste is displaced slightly fro
More informationKinetics of Rigid (Planar) Bodies
Kinetics of Rigi (Planar) Boies Types of otion Rectilinear translation Curvilinear translation Rotation about a fixe point eneral planar otion Kinetics of a Syste of Particles The center of ass for a syste
More informationEN40: Dynamics and Vibrations. Midterm Examination Tuesday March
EN4: Dynaics and Vibrations Midter Exaination Tuesday March 8 16 School of Engineering Brown University NAME: General Instructions No collaboration of any kind is peritted on this exaination. You ay bring
More informationChapter 12. Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = -kx
Chapter 1 Lecture Notes Chapter 1 Oscillatory Motion Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = -kx When the mass is released, the spring will pull
More informationQuestion number 1 to 8 carries 2 marks each, 9 to 16 carries 4 marks each and 17 to 18 carries 6 marks each.
IIT-JEE5-PH-1 FIITJEE Solutions to IITJEE 5 Mains Paper Tie: hours Physics Note: Question nuber 1 to 8 carries arks each, 9 to 16 carries 4 arks each and 17 to 18 carries 6 arks each. Q1. whistling train
More informationQ5 We know that a mass at the end of a spring when displaced will perform simple m harmonic oscillations with a period given by T = 2!
Chapter 4.1 Q1 n oscillation is any otion in which the displaceent of a particle fro a fixed point keeps changing direction and there is a periodicity in the otion i.e. the otion repeats in soe way. In
More informationChapter 1: Basics of Vibrations for Simple Mechanical Systems
Chapter 1: Basics of Vibrations for Siple Mechanical Systes Introduction: The fundaentals of Sound and Vibrations are part of the broader field of echanics, with strong connections to classical echanics,
More informationOscillations. Simple Harmonic Motion of a Mass on a Spring The equation of motion for a mass m is attached to a spring of constant k is
Dr. Alain Brizard College Physics I (PY 10) Oscillations Textbook Reference: Chapter 14 sections 1-8. Simple Harmonic Motion of a Mass on a Spring The equation of motion for a mass m is attached to a spring
More informationSimple Harmonic Motion
Siple Haronic Motion Physics Enhanceent Prograe for Gifted Students The Hong Kong Acadey for Gifted Education and Departent of Physics, HKBU Departent of Physics Siple haronic otion In echanical physics,
More informationDynamical Systems. Mechanical Systems
EE/ME/AE324: Dynamical Systems Chapter 2: Modeling Translational Mechanical Systems Common Variables Used Assumes 1 DoF per mass, i.e., all motion scalar Displacement: x ()[ t [m] Velocity: dx() t vt ()
More information= T. Oscillations and Waves. Example of an Oscillating System IB 12 IB 12
Oscillation: the vibration of an object Oscillations and Waves Eaple of an Oscillating Syste A ass oscillates on a horizontal spring without friction as shown below. At each position, analyze its displaceent,
More informationEN40: Dynamics and Vibrations. Final Examination Monday May : 2pm-5pm
EN40: Dynaics and Vibrations Final Exaination Monday May 13 013: p-5p School of Engineering Brown University NAME: General Instructions No collaboration of any kind is peritted on this exaination. You
More informationME Machine Design I. FINAL EXAM. OPEN BOOK AND CLOSED NOTES. Friday, May 8th, 2009
ME 5 - Machine Design I Spring Seester 009 Nae Lab. Div. FINAL EXAM. OPEN BOOK AND LOSED NOTES. Friday, May 8th, 009 Please use the blank paper for your solutions. Write on one side of the paper only.
More informationPhysics 207 Lecture 18. Physics 207, Lecture 18, Nov. 3 Goals: Chapter 14
Physics 07, Lecture 18, Nov. 3 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand
More informationVibrations: Second Order Systems with One Degree of Freedom, Free Response
Single Degree of Freedom System 1.003J/1.053J Dynamics and Control I, Spring 007 Professor Thomas Peacock 5//007 Lecture 0 Vibrations: Second Order Systems with One Degree of Freedom, Free Response Single
More information5/09/06 PHYSICS 213 Exam #1 NAME FEYNMAN Please write down your name also on the back side of the last page
5/09/06 PHYSICS 13 Exa #1 NAME FEYNMAN Please write down your nae also on the back side of the last page 1 he figure shows a horizontal planks of length =50 c, and ass M= 1 Kg, pivoted at one end. he planks
More informationActuators & Mechanisms Actuator sizing
Course Code: MDP 454, Course Nae:, Second Seester 2014 Actuators & Mechaniss Actuator sizing Contents - Modelling of Mechanical Syste - Mechaniss and Drives The study of Mechatronics systes can be divided
More informationl1, l2, l3, ln l1 + l2 + l3 + ln
Work done by a constant force: Consider an object undergoes a displacement S along a straight line while acted on a force F that makes an angle θ with S as shown The work done W by the agent is the product
More informationPhysics 4A Solutions to Chapter 15 Homework
Physics 4A Solutions to Chapter 15 Hoework Chapter 15 Questions:, 8, 1 Exercises & Probles 6, 5, 31, 41, 59, 7, 73, 88, 90 Answers to Questions: Q 15- (a) toward -x (b) toward +x (c) between -x and 0 (d)
More informationPhysics 121, April 3, Equilibrium and Simple Harmonic Motion. Physics 121. April 3, Physics 121. April 3, Course Information
Physics 121, April 3, 2008. Equilibrium and Simple Harmonic Motion. Physics 121. April 3, 2008. Course Information Topics to be discussed today: Requirements for Equilibrium (a brief review) Stress and
More informationFaculty of Computers and Information. Basic Science Department
18--018 FCI 1 Faculty of Computers and Information Basic Science Department 017-018 Prof. Nabila.M.Hassan 18--018 FCI Aims of Course: The graduates have to know the nature of vibration wave motions with
More informationROTATIONAL MOTION FROM TRANSLATIONAL MOTION
ROTATIONAL MOTION FROM TRANSLATIONAL MOTION Velocity Acceleration 1-D otion 3-D otion Linear oentu TO We have shown that, the translational otion of a acroscopic object is equivalent to the translational
More informationOSCILLATIONS AND WAVES
OSCILLATIONS AND WAVES OSCILLATION IS AN EXAMPLE OF PERIODIC MOTION No stories this tie, we are going to get straight to the topic. We say that an event is Periodic in nature when it repeats itself in
More informationNAME NUMBER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002. PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2 Q2 Q3 Total 40%
NAME NUMER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002 PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2.5 Q1 ( ) 2 Q2 Q3 Total 40% Use the followings: Magnitude of acceleration due to gravity
More informationChapter 14 Periodic Motion
Chapter 14 Periodic Motion 1 Describing Oscillation First, we want to describe the kinematical and dynamical quantities associated with Simple Harmonic Motion (SHM), for example, x, v x, a x, and F x.
More informationChapter 7 Work and Kinetic Energy. Copyright 2010 Pearson Education, Inc.
Chapter 7 Work and Kinetic Energy Units of Chapter 7 Work Done by a Constant Force Kinetic Energy and the Work-Energy Theorem Work Done by a Variable Force Power 7-1 Work Done by a Constant Force The definition
More informationPhysics 201, Lecture 15
Physics 0, Lecture 5 Today s Topics q More on Linear Moentu And Collisions Elastic and Perfect Inelastic Collision (D) Two Diensional Elastic Collisions Exercise: Billiards Board Explosion q Multi-Particle
More informationModern Control Systems (ECEG-4601) Instructor: Andinet Negash. Chapter 1 Lecture 3: State Space, II
Modern Control Systes (ECEG-46) Instructor: Andinet Negash Chapter Lecture 3: State Space, II Eaples Eaple 5: control o liquid levels: in cheical plants, it is oten necessary to aintain the levels o liquids.
More informationA. B. C. D. E. v x. ΣF x
Q4.3 The graph to the right shows the velocity of an object as a function of time. Which of the graphs below best shows the net force versus time for this object? 0 v x t ΣF x ΣF x ΣF x ΣF x ΣF x 0 t 0
More informationA body of unknown mass is attached to an ideal spring with force constant 123 N/m. It is found to vibrate with a frequency of
Chapter 14 [ Edit ] Overview Suary View Diagnostics View Print View with Answers Chapter 14 Due: 11:59p on Sunday, Noveber 27, 2016 To understand how points are awarded, read the Grading Policy for this
More informationPS 11 GeneralPhysics I for the Life Sciences
PS GeneralPhysics I for the Life Sciences W O R K N D E N E R G Y D R. E N J M I N C H N S S O C I T E P R O F E S S O R P H Y S I C S D E P R T M E N T J N U R Y 0 4 Questions and Probles for Conteplation
More informationKinetic Energy and Work
Kinetic Energy and Work 8.01 W06D1 Today s Readings: Chapter 13 The Concept of Energy and Conservation of Energy, Sections 13.1-13.8 Announcements Problem Set 4 due Week 6 Tuesday at 9 pm in box outside
More information3. Period Law: Simplified proof for circular orbits Equate gravitational and centripetal forces
Physics 106 Lecture 10 Kepler s Laws and Planetary Motion-continued SJ 7 th ed.: Chap 1., 1.6 Kepler s laws of planetary otion Orbit Law Area Law Period Law Satellite and planetary orbits Orbits, potential,
More informationAP Physics. Harmonic Motion. Multiple Choice. Test E
AP Physics Harmonic Motion Multiple Choice Test E A 0.10-Kg block is attached to a spring, initially unstretched, of force constant k = 40 N m as shown below. The block is released from rest at t = 0 sec.
More informationPH 221-1D Spring Oscillations. Lectures Chapter 15 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition)
PH 1-1D Spring 013 Oscillations Lectures 35-37 Chapter 15 (Halliday/Resnick/Walker, Fundaentals of Physics 9 th edition) 1 Chapter 15 Oscillations In this chapter we will cover the following topics: Displaceent,
More informationCHAPTER 12 OSCILLATORY MOTION
CHAPTER 1 OSCILLATORY MOTION Before starting the discussion of the chapter s concepts it is worth to define some terms we will use frequently in this chapter: 1. The period of the motion, T, is the time
More informationLecture Notes for PHY 405 Classical Mechanics
Lecture Notes for PHY 405 Classical Mechanics From Thorton & Marion s Classical Mechanics Prepared by Dr. Joseph M. Hahn Saint Mary s University Department of Astronomy & Physics September 1, 2005 Chapter
More informationChapter 7. Work and Kinetic Energy
Chapter 7 Work and Kinetic Energy P. Lam 7_16_2018 Learning Goals for Chapter 7 To understand the concept of kinetic energy (energy of motion) To understand the meaning of work done by a force. To apply
More informationTheoretical Basis of Modal Analysis
American Journal of Mechanical Engineering, 03, Vol., No. 7, 73-79 Available online at http://pubs.sciepub.com/ajme//7/4 Science and Education Publishing DOI:0.69/ajme--7-4 heoretical Basis of Modal Analysis
More informationWYSE Academic Challenge Sectional Physics 2006 Solution Set
WYSE Acadeic Challenge Sectional Physics 6 Solution Set. Correct answer: d. Using Newton s nd Law: r r F 6.N a.kg 6./s.. Correct answer: c. 6. sin θ 98. 3. Correct answer: b. o 37.8 98. N 6. N Using Newton
More informationEN40: Dynamics and Vibrations. Final Examination Tuesday May 15, 2011
EN40: ynaics and Vibrations Final Exaination Tuesday May 15, 011 School of Engineering rown University NME: General Instructions No collaboration of any ind is peritted on this exaination. You ay use double
More informationChapter 4. Energy. Work Power Kinetic Energy Potential Energy Conservation of Energy. W = Fs Work = (force)(distance)
Chapter 4 Energy In This Chapter: Work Kinetic Energy Potential Energy Conservation of Energy Work Work is a measure of the amount of change (in a general sense) that a force produces when it acts on a
More informationWORK, ENERGY & POWER Work scalar W = F S Cosθ Unit of work in SI system Work done by a constant force
WORK, ENERGY & POWER Work Let a force be applied on a body so that the body gets displaced. Then work is said to be done. So work is said to be done if the point of application of force gets displaced.
More informationKinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)
Kinematics (special case) a = constant 1D motion 2D projectile Uniform circular Dynamics gravity, tension, elastic, normal, friction Motion with a = constant Newton s Laws F = m a F 12 = F 21 Time & Position
More informationDr. Gundersen Phy 205DJ Test 2 22 March 2010
Signature: Idnumber: Name: Do only four out of the five problems. The first problem consists of five multiple choice questions. If you do more only your FIRST four answered problems will be graded. Clearly
More informationModeling and Simulation Revision III D R. T A R E K A. T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y, J O R D A N
Modeling and Simulation Revision III D R. T A R E K A. T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y, J O R D A N 0 1 4 Block Diagrams Block diagram models consist of two fundamental objects:
More informationSecond Order Systems
Second Order Systems independent energy storage elements => Resonance: inertance & capacitance trade energy, kinetic to potential Example: Automobile Suspension x z vertical motions suspension spring shock
More informationPhysics 1401V October 28, 2016 Prof. James Kakalios Quiz No. 2
This is a closed book, closed notes, quiz. Only simple (non-programmable, nongraphing) calculators are permitted. Define all symbols and justify all mathematical expressions used. Make sure to state all
More informationTwo-Mass, Three-Spring Dynamic System Investigation Case Study
Two-ass, Three-Spring Dynamic System Investigation Case Study easurements, Calculations, anufacturer's Specifications odel Parameter Identification Which Parameters to Identify? What Tests to Perform?
More informationConsider a particle in 1D at position x(t), subject to a force F (x), so that mẍ = F (x). Define the kinetic energy to be.
Chapter 4 Energy and Stability 4.1 Energy in 1D Consider a particle in 1D at position x(t), subject to a force F (x), so that mẍ = F (x). Define the kinetic energy to be T = 1 2 mẋ2 and the potential energy
More informationOscillations. Phys101 Lectures 28, 29. Key points: Simple Harmonic Motion (SHM) SHM Related to Uniform Circular Motion The Simple Pendulum
Phys101 Lectures 8, 9 Oscillations Key points: Simple Harmonic Motion (SHM) SHM Related to Uniform Circular Motion The Simple Pendulum Ref: 11-1,,3,4. Page 1 Oscillations of a Spring If an object oscillates
More informationChapter 15 - Oscillations
The pendulum of the mind oscillates between sense and nonsense, not between right and wrong. -Carl Gustav Jung David J. Starling Penn State Hazleton PHYS 211 Oscillatory motion is motion that is periodic
More informationCE 102: Engineering Mechanics. Minimum Potential Energy
CE 10: Engineering Mechanics Minimum Potential Energy Work of a Force During a Finite Displacement Work of a force corresponding to an infinitesimal displacement, Work of a force corresponding to a finite
More informationWileyPLUS Assignment 3. Next Week
WileyPLUS Assignent 3 Chapters 6 & 7 Due Wednesday, Noveber 11 at 11 p Next Wee No labs of tutorials Reebrance Day holiday on Wednesday (no classes) 24 Displaceent, x Mass on a spring ωt = 2π x = A cos
More informationOscillatory Motion SHM
Chapter 15 Oscillatory Motion SHM Dr. Armen Kocharian Periodic Motion Periodic motion is motion of an object that regularly repeats The object returns to a given position after a fixed time interval A
More informationChapter 13: Oscillatory Motions
Chapter 13: Oscillatory Motions Simple harmonic motion Spring and Hooe s law When a mass hanging from a spring and in equilibrium, the Newton s nd law says: Fy ma Fs Fg 0 Fs Fg This means the force due
More information2. Which of the following best describes the relationship between force and potential energy?
Work/Energy with Calculus 1. An object oves according to the function x = t 5/ where x is the distance traveled and t is the tie. Its kinetic energy is proportional to (A) t (B) t 5/ (C) t 3 (D) t 3/ (E)
More informationChapter 7 Kinetic Energy and Work
Prof. Dr. I. Nasser Chapter7_I 14/11/017 Chapter 7 Kinetic Energy and Work Energy: Measure of the ability of a body or system to do work or produce a change, expressed usually in joules or kilowatt hours
More information19. LC and RLC Oscillators
University of Rhode Island Digitaloons@URI PHY 204: Eleentary Physics II Physics ourse Materials 2015 19. L and RL Oscillators Gerhard Müller University of Rhode Island, guller@uri.edu reative oons License
More informationComb Resonator Design (4)
Lecture 8: Comb Resonator Design (4) - Intro. to Fluidic Dynamics (Damping) - School of Electrical Engineering and Computer Science, Seoul National University Nano/Micro Systems & Controls Laboratory Email:
More informationChapter 6: Work and Kinetic Energy
Chapter 6: Work and Kinetic Energy Suppose you want to find the final velocity of an object being acted on by a variable force. Newton s 2 nd law gives the differential equation (for 1D motion) dv dt =
More informationPhysics 231 Lecture 8
Shelf-life of ideas at the Bookstore Physics 31 Lecture 8 Mi Main points of today s lecture: Frictional forces: kinetic friction: fk = μk N static friction f < μs N s Work: W = FΔs cos( θ ) = FxΔx Kinetic
More informationVibrations and Waves MP205, Assignment 4 Solutions
Vibrations and Waves MP205, Assignment Solutions 1. Verify that x = Ae αt cos ωt is a possible solution of the equation and find α and ω in terms of γ and ω 0. [20] dt 2 + γ dx dt + ω2 0x = 0, Given x
More informationChapter 15. Oscillatory Motion
Chapter 15 Oscillatory Motion Part 2 Oscillations and Mechanical Waves Periodic motion is the repeating motion of an object in which it continues to return to a given position after a fixed time interval.
More informationContents. Dynamics and control of mechanical systems. Focus on
Dynamics and control of mechanical systems Date Day 1 (01/08) Day 2 (03/08) Day 3 (05/08) Day 4 (07/08) Day 5 (09/08) Day 6 (11/08) Content Review of the basics of mechanics. Kinematics of rigid bodies
More informationPhysics 140 D100 Midterm Exam 2 Solutions 2017 Nov 10
There are 10 ultiple choice questions. Select the correct answer for each one and ark it on the bubble for on the cover sheet. Each question has only one correct answer. (2 arks each) 1. An inertial reference
More informationEQUIVALENT SINGLE-DEGREE-OF-FREEDOM SYSTEM AND FREE VIBRATION
1 EQUIVALENT SINGLE-DEGREE-OF-FREEDOM SYSTEM AND FREE VIBRATION The course on Mechanical Vibration is an important part of the Mechanical Engineering undergraduate curriculum. It is necessary for the development
More informationMechanics 2 Aide Memoire. Work done = or Fx for a constant force, F over a distance, x. = or Pt for constant power, P over t seconds
Mechanics 2 Aide Memoire Work done measured in Joules Energy lost due to overcoming a force (no work done if force acts perpendicular to the direction of motion) Work done = or Fx for a constant force,
More informationdt dt THE AIR TRACK (II)
THE AIR TRACK (II) References: [] The Air Track (I) - First Year Physics Laoratory Manual (PHY38Y and PHYY) [] Berkeley Physics Laoratory, nd edition, McGraw-Hill Book Copany [3] E. Hecht: Physics: Calculus,
More informationIn this chapter we will start the discussion on wave phenomena. We will study the following topics:
Chapter 16 Waves I In this chapter we will start the discussion on wave phenoena. We will study the following topics: Types of waves Aplitude, phase, frequency, period, propagation speed of a wave Mechanical
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PH105-007 Exam 2 VERSION A Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal
More information