ESCI 343 Atmospheric Dynamics II Lesson 8 Sound Waves
|
|
|
- Cory Moore
- 6 years ago
- Views:
Transcription
1 ESCI 343 Amoheri Dynami II Leon 8 Sond Wae Referene: An Inrodion o Dynami Meeorology (3 rd ediion), JR Holon Wae in Flid, J Lighhill SOUND WAVES We will limi or analyi o ond wae raeling only along he -ai, b kee in mind ha we old eaily eend hi o wae raeling in an arbirary direion We ar wih he linearized eqaion of moion for he ae of zero mean flow, and for whih he referene deniy i onan wih heigh Thee are () We alo hae an eqaion of ae ha relae any hree of he hermodynami ariable We will e,, and a or hermodynami ariable, o or eqaion of ae an be wrien a (, ) The eqaion of ae an be wrien in differenial form a d d d () Sond wae are adiabai, o ha i onan Therefore, we an wrie or in linearized form d d d d (3) If we bie hi ino he oniniy eqaion, he linearized e of eqaion for onedimenional ond wae are hen (4)
2 To find he dierion relaion for ond wae we ame inoidal olion of i( k ) Ae (5) i( k ) Be and bie hem ino he wo rior eqaion o find ha hee are nondierie wae raelling a a hae eed of (6) Sine we know ha hee are ond wae, we hae hown ha for a general flid he eed of ond i gien by (7) Thi how ha he eed of ond i fndamenal roery of a flid I alo how ha ond wae are non-dierie THE CONTINUITY EQUATION WRITTEN WITH THE SPEED OF SOUND Uing Eq () and (7) we an wrie D D (8) D D whih allow o ere he flly omreible oniniy eqaion in erm of he maerial deriaie of rere, D V (9) D Thi i a ommon way of wriing he oniniy eqaion THE SPEED OF SOUND IN AN IDEAL GAS In an ideal ga, he eqaion of ae ha he form RT (0) In erm of oenial emerare, hi an be wrien a R 0 R () Aally, we e only hown ha linear ond wae are nondierie We haen, and won di any of he effe of non-linear ond wae
3 Taking he arial deriaie of hi wih ree o deniy a onan oenial emerare, and making e of he fa ha for an ideal ga = + R, afer ome aiene yo an find ha for an ideal ga, he eed of ond i gien by RT () (3) SOUND WAVES WITH A NON-ZERO MEAN FLOW So far we e ignored he mean flow If here i a bai ae mean flow hen he analyi i lighly more omle Or linearized eqaion of moion beome (4) Remember ha or goal i o find he dierion relaion for he wae We do o by aming a inoidal form for boh deenden ariable, of he form of Eq (5) and bie hee direly ino Eq (4) The rel i he following dierion relaion, k (5) Noe ha he effe of he mean flow i addiie Thi i a roery of linear wae For linear wae, he hae eed wih mean flow i j he hae eed wiho he mean flow l he mean flow ielf VERTICALLY PROPOGATING SOUND WAVES For ond wae roagaing in all hree dimenion he linearized goerning eqaion are y (6) w g z w w z y z For ffiienly large wae nmber (ffiienly mall waelengh) i rn o ha we an ignore he effe of boyany (graiy) and he erial gradien of he referene rere In raial erm hi mean a long a he wae are ffiienly hor h 3
4 ha he waelengh i mall omared o he ale oer whih rere and deniy hange wih heigh, or (7) z (deail an be fond in Lighhill, Seion 4) Condiion (7) an be ereed a H (8) where H i he deniy ale heigh of he amohere So, a long a we limi orele o ond wae in he normal range of hman hearing we an ignore he effe of graiy on ond wae Or eqaion are hen y (9) w z w y z Sbiing inoidal form for,, w, and of iklymz Ae Be w Ce De i klymz i klymz i klymz (0) yield he following dierion relaion k l m K () Deniy ale heigh i he e-folding ale for deniy, ie, he alide a whih deniy i 37% of he rfae ale 4
5 5 EXERCISES The linearized goerning eqaion for one-dimenional ond wae wih zero mean flow are Sbie he amed olion k i k i Be Ae ino hee eqaion o derie he dierion relaion for ond wae The linearized goerning eqaion for hree-dimenional ond wae wih zero mean flow are z w y z w y Derie he dierion relaion m l k for hee wae 3 Show ha he eed of ond in an ideal ga i R T 4 Show ha for an iohermal amohere ha Condiion (7) beome Condiion (8) 5 a Find he ale heigh and eed of ond for an iohermal amohere wih a emerare of 55K b For hi amohere, find o how large he waelengh of an aoi wae wold need o be before we ared onerning orele wih he effe of graiy and boyany on hee wae
PHYS-3301 Lecture 5. Chapter 2. Announcement. Sep. 12, Special Relativity. What about y and z coordinates? (x - direction of motion)
Announemen Course webpage hp://www.phys.u.edu/~slee/33/ Tebook PHYS-33 Leure 5 HW (due 9/4) Chaper, 6, 36, 4, 45, 5, 5, 55, 58 Sep., 7 Chaper Speial Relaiiy. Basi Ideas. Consequenes of Einsein s Posulaes
8.1. a) For step response, M input is u ( t) Taking inverse Laplace transform. as α 0. Ideal response, K c. = Kc Mτ D + For ramp response, 8-1
8. a For ep repone, inpu i u, U Y a U α α Y a α α Taking invere Laplae ranform a α e e / α / α A α 0 a δ 0 e / α a δ deal repone, α d Y i Gi U i δ Hene a α 0 a i For ramp repone, inpu i u, U Soluion anual
Generalized The General Relativity Using Generalized Lorentz Transformation
P P P P IJISET - Inernaional Journal of Innoaie Siene, Engineering & Tehnology, Vol. 3 Issue 4, April 6. www.ijise.om ISSN 348 7968 Generalized The General Relaiiy Using Generalized Lorenz Transformaion
INSTANTANEOUS VELOCITY
INSTANTANEOUS VELOCITY I claim ha ha if acceleraion is consan, hen he elociy is a linear funcion of ime and he posiion a quadraic funcion of ime. We wan o inesigae hose claims, and a he same ime, work
Derivation of longitudinal Doppler shift equation between two moving bodies in reference frame at rest
Deriaion o longiudinal Doppler shi equaion beween wo moing bodies in reerene rame a res Masanori Sao Honda Eleronis Co., d., Oyamazuka, Oiwa-ho, Toyohashi, ihi 44-393, Japan E-mail: msao@honda-el.o.jp
Lecture 2: Telegrapher Equations For Transmission Lines. Power Flow.
Whies, EE 481/581 Lecure 2 Page 1 of 13 Lecure 2: Telegraher Equaions For Transmission Lines. Power Flow. Microsri is one mehod for making elecrical connecions in a microwae circui. I is consruced wih
EFFECT OF PILE SPACING ON PILE BEHAVIOR UNDER DYNAMIC LOADS
The 4 h World Conferene on Earhqake Engineering Oober -7, 8, eiing, China EFFECT OF PILE SPACIN ON PILE EHAVIO UNDE DYNAIC LOADS S. üçükarlan and P.. aneree Aoiae Profeor, De. of Engineering Siene, Ianbl
Chapter 12: Velocity, acceleration, and forces
To Feel a Force Chaper Spring, Chaper : A. Saes of moion For moion on or near he surface of he earh, i is naural o measure moion wih respec o objecs fixed o he earh. The 4 hr. roaion of he earh has a measurable
PHYSICS 151 Notes for Online Lecture #4
PHYSICS 5 Noe for Online Lecure #4 Acceleraion The ga pedal in a car i alo called an acceleraor becaue preing i allow you o change your elociy. Acceleraion i how fa he elociy change. So if you ar fro re
Topic 1: Linear motion and forces
TOPIC 1 Topic 1: Linear moion and forces 1.1 Moion under consan acceleraion Science undersanding 1. Linear moion wih consan elociy is described in erms of relaionships beween measureable scalar and ecor
On Line Supplement to Strategic Customers in a Transportation Station When is it Optimal to Wait? A. Manou, A. Economou, and F.
On Line Spplemen o Sraegic Comer in a Tranporaion Saion When i i Opimal o Wai? A. Mano, A. Economo, and F. Karaemen 11. Appendix In hi Appendix, we provide ome echnical analic proof for he main rel of
One-Dimensional Kinematics
One-Dimensional Kinemaics One dimensional kinemaics refers o moion along a sraigh line. Een hough we lie in a 3-dimension world, moion can ofen be absraced o a single dimension. We can also describe moion
Coupled Mass Transport and Reaction in LPCVD Reactors
ople Ma Tanpo an eaion in LPV eao ile A in B e.g., SiH 4 in H Sepaae eao ino o egion, inaafe & annla b - oniniy Eqn: : onveion-iffion iffion-eaion Eqn Ampion! ile peie i in majo aie ga e.g., H isih 4!
Differential Geometry: Revisiting Curvatures
Differenial Geomery: Reisiing Curaures Curaure and Graphs Recall: hus, up o a roaion in he x-y plane, we hae: f 1 ( x, y) x y he alues 1 and are he principal curaures a p and he corresponding direcions
Kinematics of Wheeled Robots
1 Kinemaics of Wheeled Robos hps://www.ouube.com/wach?=gis41ujlbu 2 Wheeled Mobile Robos robo can hae one or more wheels ha can proide seering direcional conrol power eer a force agains he ground an ideal
EECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signal & Syem Prof. Mark Fowler Noe Se #27 C-T Syem: Laplace Tranform Power Tool for yem analyi Reading Aignmen: Secion 6.1 6.3 of Kamen and Heck 1/18 Coure Flow Diagram The arrow here how concepual
Learning from a Golf Ball
Session 1566 Learning from a Golf Ball Alireza Mohammadzadeh Padnos School of Engineering Grand Valley Sae Uniersiy Oeriew Projecile moion of objecs, in he absence of air fricion, is sdied in dynamics
The Special Theory of Relativity Chapter II
The Speial Theory of Relaiiy Chaper II 1. Relaiisi Kinemais. Time dilaion and spae rael 3. Lengh onraion 4. Lorenz ransformaions 5. Paradoes? Simulaneiy/Relaiiy If one obserer sees he eens as simulaneous,
Module 2 F c i k c s la l w a s o s f dif di fusi s o i n
Module Fick s laws of diffusion Fick s laws of diffusion and hin film soluion Adolf Fick (1855) proposed: d J α d d d J (mole/m s) flu (m /s) diffusion coefficien and (mole/m 3 ) concenraion of ions, aoms
Elementary non-linear processes in aero-acoustics of internal flows
Elemenary non-linear roee in aero-aoi of inernal flow Avraham Mio Hirhberg Tehnihe Univeriei Eindhoven Workho N3L, 7- may TU Münhen Oline. Wave diorion -D friionle hok wave. Driven reonane in loed ie b-harmoni
MODEL PAPER 2 PHYSICS. I PUC Time: 3 hours Max Marks: 70
MODEL PAPE PHYSICS I PUC Time: hour Ma Mark: 7 General Inrucion: i) All par are compulory. ii) Anwer wihou relean diagram / figure/ circui whereer neceary will no carry any mark. iii) Direc anwer o he
Math Week 14 April 16-20: sections first order systems of linear differential equations; 7.4 mass-spring systems.
Mah 2250-004 Week 4 April 6-20 secions 7.-7.3 firs order sysems of linear differenial equaions; 7.4 mass-spring sysems. Mon Apr 6 7.-7.2 Sysems of differenial equaions (7.), and he vecor Calculus we need
2. VECTORS. R Vectors are denoted by bold-face characters such as R, V, etc. The magnitude of a vector, such as R, is denoted as R, R, V
ME 352 VETS 2. VETS Vecor algebra form he mahemaical foundaion for kinemaic and dnamic. Geomer of moion i a he hear of boh he kinemaic and dnamic of mechanical em. Vecor anali i he imehonored ool for decribing
Introduction to SLE Lecture Notes
Inroducion o SLE Lecure Noe May 13, 16 - The goal of hi ecion i o find a ufficien condiion of λ for he hull K o be generaed by a imple cure. I urn ou if λ 1 < 4 hen K i generaed by a imple curve. We will
Solution of Integro-Differential Equations by Using ELzaki Transform
Global Journal of Mahemaical Sciences: Theory and Pracical. Volume, Number (), pp. - Inernaional Research Publicaion House hp://www.irphouse.com Soluion of Inegro-Differenial Equaions by Using ELzaki Transform
Section 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
Secion 3.5 Nonhomogeneous Equaions; Mehod of Undeermined Coefficiens Key Terms/Ideas: Linear Differenial operaor Nonlinear operaor Second order homogeneous DE Second order nonhomogeneous DE Soluion o homogeneous
Chapter 8 The Complete Response of RL and RC Circuits
Chaper 8 he Complee Response of R and RC Ciruis Exerises Ex 8.3-1 Before he swih loses: Afer he swih loses: 2 = = 8 Ω so = 8 0.05 = 0.4 s. 0.25 herefore R ( ) Finally, 2.5 ( ) = o + ( (0) o ) = 2 + V for
Chapter 2. First Order Scalar Equations
Chaper. Firs Order Scalar Equaions We sar our sudy of differenial equaions in he same way he pioneers in his field did. We show paricular echniques o solve paricular ypes of firs order differenial equaions.
2.3 The Lorentz Transformation Eq.
Announemen Course webage h://highenergy.hys.u.edu/~slee/4/ Tebook PHYS-4 Leure 4 HW (due 9/3 Chaer, 6, 36, 4, 45, 5, 5, 55, 58 Se. 8, 6.3 The Lorenz Transformaion q. We an use γ o wrie our ransformaions.
To become more mathematically correct, Circuit equations are Algebraic Differential equations. from KVL, KCL from the constitutive relationship
Laplace Tranform (Lin & DeCarlo: Ch 3) ENSC30 Elecric Circui II The Laplace ranform i an inegral ranformaion. I ranform: f ( ) F( ) ime variable complex variable From Euler > Lagrange > Laplace. Hence,
FLAT CYCLOTOMIC POLYNOMIALS OF ORDER FOUR AND HIGHER
#A30 INTEGERS 10 (010), 357-363 FLAT CYCLOTOMIC POLYNOMIALS OF ORDER FOUR AND HIGHER Nahan Kaplan Deparmen of Mahemaic, Harvard Univeriy, Cambridge, MA nkaplan@mah.harvard.edu Received: 7/15/09, Revied:
Identification of the Solution of the Burgers. Equation on a Finite Interval via the Solution of an. Appropriate Stochastic Control Problem
Ad. heor. Al. Mech. Vol. 3 no. 37-44 Idenificaion of he oluion of he Burger Equaion on a Finie Ineral ia he oluion of an Aroriae ochaic Conrol roblem Arjuna I. Ranainghe Dearmen of Mahemaic Alabama A &
THE BERNOULLI NUMBERS. t k. = lim. = lim = 1, d t B 1 = lim. 1+e t te t = lim t 0 (e t 1) 2. = lim = 1 2.
THE BERNOULLI NUMBERS The Bernoulli numbers are defined here by he exponenial generaing funcion ( e The firs one is easy o compue: (2 and (3 B 0 lim 0 e lim, 0 e ( d B lim 0 d e +e e lim 0 (e 2 lim 0 2(e
LIGHT and SPECIAL RELATIVITY
VISUAL PHYSICS ONLINE MODULE 7 NATURE OF LIGHT LIGHT and SPECIAL RELATIVITY LENGTH CONTRACTION RELATIVISTIC ADDITION OF VELOCITIES Time is a relaie quaniy: differen obserers an measuremen differen ime
Newtonian Relativity
Newonian Relaii A referene frame in whih Newon s laws are alid is alled an inerial frame Newonian priniple of relaii or Galilean inariane If Newon s laws are alid in one referene frame, hen he are also
TP B.2 Rolling resistance, spin resistance, and "ball turn"
echnical proof TP B. olling reiance, pin reiance, and "ball urn" upporing: The Illuraed Principle of Pool and Billiard hp://billiard.coloae.edu by Daid G. Alciaore, PhD, PE ("Dr. Dae") echnical proof originally
MEI STRUCTURED MATHEMATICS 4758
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Cerificae of Educaion Advanced General Cerificae of Educaion MEI STRUCTURED MATHEMATICS 4758 Differenial Equaions Thursday 5 JUNE 006 Afernoon
4.6 One Dimensional Kinematics and Integration
4.6 One Dimensional Kinemaics and Inegraion When he acceleraion a( of an objec is a non-consan funcion of ime, we would like o deermine he ime dependence of he posiion funcion x( and he x -componen of
The Full Mathematics of: SPECIAL Relativity. By: PRASANNA PAKKIAM
The Fll Mahemais of: SPECIL Relaii : PRSNN PKKIM CONTENTS INTRODUCTION 3 TIME DILTION & LENGTH CONTRCTION 4 LORENZ TRNSFORMTIONS & COMPOSITION OF VELOCITIES 6 RELTIVISTIC MSS RELTIVISTIC ENERGY 3 ibliograph
Amit Mehra. Indian School of Business, Hyderabad, INDIA Vijay Mookerjee
RESEARCH ARTICLE HUMAN CAPITAL DEVELOPMENT FOR PROGRAMMERS USING OPEN SOURCE SOFTWARE Ami Mehra Indian Shool of Business, Hyderabad, INDIA {Ami_Mehra@isb.edu} Vijay Mookerjee Shool of Managemen, Uniersiy
1 First Order Partial Differential Equations
Firs Order Parial Differenial Eqaions The profond sdy of nare is he mos ferile sorce of mahemaical discoveries. - Joseph Forier (768-830). Inrodcion We begin or sdy of parial differenial eqaions wih firs
LAB # 2 - Equilibrium (static)
AB # - Equilibrium (saic) Inroducion Isaac Newon's conribuion o physics was o recognize ha despie he seeming compleiy of he Unierse, he moion of is pars is guided by surprisingly simple aws. Newon's inspiraion
total distance cov ered time int erval v = average speed (m/s)
Physics Suy Noes Lesson 4 Linear Moion 1 Change an Moion a. A propery common o eeryhing in he unierse is change. b. Change is so imporan ha he funamenal concep of ime woul be meaningless wihou i. c. Since
Graphs III - Network Flow
Graph III - Nework Flow Flow nework eup graph G=(V,E) edge capaciy w(u,v) 0 - if edge doe no exi, hen w(u,v)=0 pecial verice: ource verex ; ink verex - no edge ino and no edge ou of Aume every verex v
arxiv:physics/ v1 [physics.ed-ph] 6 Feb 2004
![arxiv:physics/ v1 [physics.ed-ph] 6 Feb 2004](/thumbs/85/91938492.jpg "arxiv:physics/ v1 [physics.ed-ph] 6 Feb 2004")
The Herz conac in chain elasic collisions P. Parício Insiuo Superior de Engenharia de Lisboa Rua Conselheiro Emídio Naarro, P-949-4 Lisboa, Porugal (January 4) arxi:physics/46 [physics.ed-ph] 6 Feb 4 A
v 1 =4 m/s v 2 =0 m 1 =0.5kg m 2 Momentum F (N) t (s) v 0y v x
Moenu Do our work on a earae hee of aer or noebook. or each roble, draw clearl labeled diagra howing he ae and elociie for each objec before and afer he colliion. Don forge abou direcion oenu, eloci and
Atmospheric Dynamics 11:670:324. Class Time: Tuesdays and Fridays 9:15-10:35
Amospheric Dnamics 11:67:324 Class ime: esdas and Fridas 9:15-1:35 Insrcors: Dr. Anhon J. Broccoli (ENR 229 broccoli@ensci.rgers.ed 848-932-5749 Dr. Benjamin Linner (ENR 25 linner@ensci.rgers.ed 848-932-5731
Module 2: Analysis of Stress
Module/Leon Module : Anali of Sre.. INTRODUCTION A bod under he acion of eernal force, undergoe diorion and he effec due o hi em of force i ranmied hroughou he bod developing inernal force in i. To eamine
Two Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a
Kinemaics Paper 1 1. The graph below shows he ariaion wih ime of he acceleraion a of an objec from = o = T. a T The shaded area under he graph represens change in A. displacemen. B. elociy. C. momenum.
PROBLEMS ON RECTILINEAR MOTION
PROBLEMS ON RECTILINEAR MOTION PROBLEM 1. The elociy of a paricle which oe along he -ai i gien by 5 (/). Ealuae he diplaceen elociy and acceleraion a when = 4. The paricle i a he origin = when =. (/) /
EE Control Systems LECTURE 2
Copyrigh F.L. Lewi 999 All righ reerved EE 434 - Conrol Syem LECTURE REVIEW OF LAPLACE TRANSFORM LAPLACE TRANSFORM The Laplace ranform i very ueful in analyi and deign for yem ha are linear and ime-invarian
The Contradiction within Equations of Motion with Constant Acceleration
The Conradicion wihin Equaions of Moion wih Consan Acceleraion Louai Hassan Elzein Basheir (Daed: July 7, 0 This paper is prepared o demonsrae he violaion of rules of mahemaics in he algebraic derivaion
Dispersive Systems. 1) Schrödinger equation 2) Cubic Schrödinger 3) KdV 4) Discreterised hyperbolic equation 5) Discrete systems.
Dispersive Sysems 1) Schrödinger eqaion ) Cbic Schrödinger 3) KdV 4) Discreerised hyperbolic eqaion 5) Discree sysems KdV + + ε =, = ( ) ( ) d d + = d d =, =. ( ) = ( ) DISCONTINUITY, prescribed cri Collision
Physics Notes - Ch. 2 Motion in One Dimension
Physics Noes - Ch. Moion in One Dimension I. The naure o physical quaniies: scalars and ecors A. Scalar quaniy ha describes only magniude (how much), NOT including direcion; e. mass, emperaure, ime, olume,
Integration of the equation of motion with respect to time rather than displacement leads to the equations of impulse and momentum.
Inegraion of he equaion of moion wih respec o ime raher han displacemen leads o he equaions of impulse and momenum. These equaions greal faciliae he soluion of man problems in which he applied forces ac
ES.1803 Topic 22 Notes Jeremy Orloff
ES.83 Topic Noes Jeremy Orloff Fourier series inroducion: coninued. Goals. Be able o compue he Fourier coefficiens of even or odd periodic funcion using he simplified formulas.. Be able o wrie and graph
INTRODUCTION TO INERTIAL CONFINEMENT FUSION
INTODUCTION TO INETIAL CONFINEMENT FUSION. Bei Lecure 7 Soluion of he imple dynamic igniion model ecap from previou lecure: imple dynamic model ecap: 1D model dynamic model ρ P() T enhalpy flux ino ho
ME 425: Aerodynamics
ME 45: Aerodnamics Dr. A.B.M. Toiqe Hasan Proessor Deparmen o Mechanical Engineering Bangladesh Uniersi o Engineering & Technolog BUET, Dhaka Lecre-7 Fndamenals so Aerodnamics oiqehasan.be.ac.bd oiqehasan@me.be.ac.bd
, the. L and the L. x x. max. i n. It is easy to show that these two norms satisfy the following relation: x x n x = (17.3) max
ecure 8 7. Sabiliy Analyi For an n dimenional vecor R n, he and he vecor norm are defined a: = T = i n i (7.) I i eay o how ha hee wo norm aify he following relaion: n (7.) If a vecor i ime-dependen, hen
Chapter #1 EEE8013 EEE3001. Linear Controller Design and State Space Analysis
Chaper EEE83 EEE3 Chaper # EEE83 EEE3 Linear Conroller Design and Sae Space Analysis Ordinary Differenial Equaions.... Inroducion.... Firs Order ODEs... 3. Second Order ODEs... 7 3. General Maerial...
CMPS 6610/4610 Fall Flow Networks. Carola Wenk Slides adapted from slides by Charles Leiserson
CMP 6610/4610 Fall 2016 Flow Nework Carola Wenk lide adaped rom lide by Charle Leieron Max low and min c Fndamenal problem in combinaorial opimizaion Daliy beween max low and min c Many applicaion: Biparie
Complete solutions to Exercise 14(b) 1. Very similar to EXAMPLE 4. We have same characteristic equation:
Soluions 4(b) Complee soluions o Exercise 4(b). Very similar o EXAMPE 4. We have same characerisic equaion: 5 i Ae = + Be By using he given iniial condiions we obain he simulaneous equaions A+ B= 0 5A
Basic solution to Heat Diffusion In general, one-dimensional heat diffusion in a material is defined by the linear, parabolic PDE
New Meio e yd 5 ydrology Program Quaniaie Meods in ydrology Basi soluion o ea iffusion In general one-dimensional ea diffusion in a maerial is defined by e linear paraboli PE or were we assume a is defined
Discussion Session 2 Constant Acceleration/Relative Motion Week 03
PHYS 100 Dicuion Seion Conan Acceleraion/Relaive Moion Week 03 The Plan Today you will work wih your group explore he idea of reference frame (i.e. relaive moion) and moion wih conan acceleraion. You ll
CSE 5365 Computer Graphics. Take Home Test #1
CSE 5365 Comper Graphics Take Home Tes #1 Fall/1996 Tae-Hoon Kim roblem #1) A bi-cbic parameric srface is defined by Hermie geomery in he direcion of parameer. In he direcion, he geomery ecor is defined
Math 10B: Mock Mid II. April 13, 2016
Name: Soluions Mah 10B: Mock Mid II April 13, 016 1. ( poins) Sae, wih jusificaion, wheher he following saemens are rue or false. (a) If a 3 3 marix A saisfies A 3 A = 0, hen i canno be inverible. True.
Mocanu Paradox of Different Types of Lorentz Transformations
Page Moanu Parado of Differen Types of Lorenz Transformaions A R aizid and M S Alam * Deparmen of usiness Adminisraion Leading niersiy Sylhe 300 angladesh Deparmen of Physis Shahjalal niersiy of Siene
Key Chemistry 102 Discussion #4, Chapter 11 and 12 Student name TA name Section. ; u= M. and T(red)=2*T(yellow) ; t(yellow)=4*t(red) or
Key Chemisry 0 Discssion #4, Chaper and Sden name TA name Secion. Two idenical conainers, one red and one yellow, are inflaed wih differen gases a he same volme and pressre. Boh conainers have an idenically
You have met function of a single variable f(x), and calculated the properties of these curves such as
Chaper 5 Parial Derivaive You have me funcion of a ingle variable f(, and calculaed he properie of hee curve uch a df d. Here we have a fir look a hee idea applied o a funcion of wo variable f(,. Graphicall
Week 1 Lecture 2 Problems 2, 5. What if something oscillates with no obvious spring? What is ω? (problem set problem)
Week 1 Lecure Problems, 5 Wha if somehing oscillaes wih no obvious spring? Wha is ω? (problem se problem) Sar wih Try and ge o SHM form E. Full beer can in lake, oscillaing F = m & = ge rearrange: F =
Let us start with a two dimensional case. We consider a vector ( x,
Roaion marices We consider now roaion marices in wo and hree dimensions. We sar wih wo dimensions since wo dimensions are easier han hree o undersand, and one dimension is a lile oo simple. However, our
MATH 31B: MIDTERM 2 REVIEW. x 2 e x2 2x dx = 1. ue u du 2. x 2 e x2 e x2] + C 2. dx = x ln(x) 2 2. ln x dx = x ln x x + C. 2, or dx = 2u du.
![MATH 31B: MIDTERM 2 REVIEW. x 2 e x2 2x dx = 1. ue u du 2. x 2 e x2 e x2] + C 2. dx = x ln(x) 2 2. ln x dx = x ln x x + C. 2, or dx = 2u du.](/thumbs/86/93221008.jpg "MATH 31B: MIDTERM 2 REVIEW. x 2 e x2 2x dx = 1. ue u du 2. x 2 e x2 e x2] + C 2. dx = x ln(x) 2 2. ln x dx = x ln x x + C. 2, or dx = 2u du.")
MATH 3B: MIDTERM REVIEW JOE HUGHES. Inegraion by Pars. Evaluae 3 e. Soluion: Firs make he subsiuion u =. Then =, hence 3 e = e = ue u Now inegrae by pars o ge ue u = ue u e u + C and subsiue he definiion
Chapter 3 Kinematics in Two Dimensions
Chaper 3 KINEMATICS IN TWO DIMENSIONS PREVIEW Two-dimensional moion includes objecs which are moing in wo direcions a he same ime, such as a projecile, which has boh horizonal and erical moion. These wo
Kinematics in two dimensions
Lecure 5 Phsics I 9.18.13 Kinemaics in wo dimensions Course websie: hp://facul.uml.edu/andri_danlo/teaching/phsicsi Lecure Capure: hp://echo36.uml.edu/danlo13/phsics1fall.hml 95.141, Fall 13, Lecure 5
Course II. Lesson 7 Applications to Physics. 7A Velocity and Acceleration of a Particle
Course II Lesson 7 Applicaions o Physics 7A Velociy and Acceleraion of a Paricle Moion in a Sraigh Line : Velociy O Aerage elociy Moion in he -ais + Δ + Δ 0 0 Δ Δ Insananeous elociy d d Δ Δ Δ 0 lim [ m/s
CONTROL SYSTEMS. Chapter 10 : State Space Response
CONTROL SYSTEMS Chaper : Sae Space Repone GATE Objecive & Numerical Type Soluion Queion 5 [GATE EE 99 IIT-Bombay : Mark] Conider a econd order yem whoe ae pace repreenaion i of he form A Bu. If () (),
Equations of motion for constant acceleration
Lecure 3 Chaper 2 Physics I 01.29.2014 Equaions of moion for consan acceleraion Course websie: hp://faculy.uml.edu/andriy_danylo/teaching/physicsi Lecure Capure: hp://echo360.uml.edu/danylo2013/physics1spring.hml
Announcements. Lecture 6 Chapter. 2 Special Relativity. Relativistic Dynamics. Relativistic Kinetic Energy. Relativistic Momentum
Announemens HW: Ch.-70, 75, 76, 87, 9, 97, 99, 104, 111 HW1 due: now, HW due: /08 (by lass hour) No lab his week; New TA (Ganga) Physis Colloquium (Thursday a 3:40m) Quiz 1: Feb 8 h. (30 min) -- Cha. ***
Conservation Laws and Hamiltonian Symmetries of Whitham-Broer-Kaup Equations
Indian Jornal of Science and Technology Vol 8( 78 84 Janary 05 ISSN (Prin : 0974-84 ISSN (Online : 0974-545 DOI : 0.7485/ijs/05/8i/47809 Conseraion Laws and Hamilonian Symmeries of Whiham-Broer-Kap Eqaions
Some Basic Information about M-S-D Systems
Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,
Notes on cointegration of real interest rates and real exchange rates. ρ (2)
Noe on coinegraion of real inere rae and real exchange rae Charle ngel, Univeriy of Wiconin Le me ar wih he obervaion ha while he lieraure (mo prominenly Meee and Rogoff (988) and dion and Paul (993))
13.1 Accelerating Objects
13.1 Acceleraing Objec A you learned in Chaper 12, when you are ravelling a a conan peed in a raigh line, you have uniform moion. However, mo objec do no ravel a conan peed in a raigh line o hey do no
THE DARBOUX TRIHEDRONS OF REGULAR CURVES ON A REGULAR TIME-LIKE SURFACE. Emin Özyilmaz
Mahemaical and Compaional Applicaions, Vol. 9, o., pp. 7-8, 04 THE DARBOUX TRIHEDROS OF REULAR CURVES O A REULAR TIME-LIKE SURFACE Emin Özyilmaz Deparmen of Mahemaics, Facly of Science, Ee Uniersiy, TR-500
Relativistic Dynamics
Announemen Course webage h://highenergy.hys.u.edu/~slee/4/ Tebook PHYS-4 Leure Se., 5 Leure Noes, HW Assignmens, Physis Colloquium, e.. Relaiisi Dynamis Chaer Seial Relaiiy. Basi Ideas. Consequenes of
ODEs II, Lecture 1: Homogeneous Linear Systems - I. Mike Raugh 1. March 8, 2004
ODEs II, Lecure : Homogeneous Linear Sysems - I Mike Raugh March 8, 4 Inroducion. In he firs lecure we discussed a sysem of linear ODEs for modeling he excreion of lead from he human body, saw how o ransform
18.03SC Unit 3 Practice Exam and Solutions
Sudy Guide on Sep, Dela, Convoluion, Laplace You can hink of he ep funcion u() a any nice mooh funcion which i for < a and for > a, where a i a poiive number which i much maller han any ime cale we care
IB Physics Kinematics Worksheet
IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?
Yukio SANOMURA. and Kunio HAYAKAWA 1/7 , 53-2, (2004-2),
/7 Modifiaion of Ioroi Hardening Model and Aliaion of Kinemai Hardening Model o Coniuive Equaion for Plai Behavior of Hydroai-Preure-Deenden Polymer by Yuio SANOMURA and Kunio HAYAKAWA Hydroai reure deendene
Kinematics. introduction to kinematics 15A
15 15A Inroducion o kinemaics 15B Velociy ime graphs and acceleraion ime graphs 15C Consan acceleraion formulas 15D Insananeous raes of change Kinemaics AreAS of STuDy Diagrammaic and graphical represenaion
8. Basic RL and RC Circuits
8. Basic L and C Circuis This chaper deals wih he soluions of he responses of L and C circuis The analysis of C and L circuis leads o a linear differenial equaion This chaper covers he following opics
Energy Momentum Tensor for Photonic System
018 IJSST Volume 4 Issue 10 Prin ISSN : 395-6011 Online ISSN : 395-60X Themed Seion: Siene and Tehnology Energy Momenum Tensor for Phooni Sysem ampada Misra Ex-Gues-Teaher, Deparmens of Eleronis, Vidyasagar
Lecture 13 RC/RL Circuits, Time Dependent Op Amp Circuits
Lecure 13 RC/RL Circuis, Time Dependen Op Amp Circuis RL Circuis The seps involved in solving simple circuis conaining dc sources, resisances, and one energy-sorage elemen (inducance or capaciance) are:
Let. x y. denote a bivariate time series with zero mean.
Linear Filer Le x y : T denoe a bivariae ime erie wih zero mean. Suppoe ha he ime erie {y : T} i conruced a follow: y a x The ime erie {y : T} i aid o be conruced from {x : T} by mean of a Linear Filer.
1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Outline 10 Torsion, Shear, and Flexure
.54/.54 Mehani and Deign of Conree Srre Spring 4 Prof. Oral Bkozrk Maahe Inie of ehnolog Oline.54/.54 Mehani and Deign of Conree Srre (3--9) Oline orion, Shear, and Flere orion o Sre diribion on a ro eion
ME 321: FLUID MECHANICS-I
8/7/18 ME 31: FLUID MECHANICS-I Dr. A.B.M. Toiqe Hasan Proessor Dearmen o Mechanical Engineering Bangladesh Uniersi o Engineering & Technolog BUET, Dhaka Lecre-13 8/7/18 Dierenial Analsis o Flid Moion
ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 2
ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER Seion Eerise -: Coninuiy of he uiliy funion Le λ ( ) be he monooni uiliy funion defined in he proof of eisene of uiliy funion If his funion is oninuous y hen
Chapter 6. Systems of First Order Linear Differential Equations
Chaper 6 Sysems of Firs Order Linear Differenial Equaions We will only discuss firs order sysems However higher order sysems may be made ino firs order sysems by a rick shown below We will have a sligh
Wall. x(t) f(t) x(t = 0) = x 0, t=0. which describes the motion of the mass in absence of any external forcing.
MECHANICS APPLICATIONS OF SECOND-ORDER ODES 7 Mechanics applicaions of second-order ODEs Second-order linear ODEs wih consan coefficiens arise in many physical applicaions. One physical sysems whose behaviour
ME 391 Mechanical Engineering Analysis
Fall 04 ME 39 Mechanical Engineering Analsis Eam # Soluions Direcions: Open noes (including course web posings). No books, compuers, or phones. An calculaor is fair game. Problem Deermine he posiion of