Titre :	Handout Waves and vibrations ; course
Type de document :	texte imprimé
Auteurs :	Amer Saoudi
Année de publication :	2026
Importance :	1 vol (84 p .)
Format :	29 cm
Langues :	Anglais (eng)
Catégories :	Publications pédagogiques:Physique P/P
Mots-clés :	Handout Waves
Index. décimale :	530-Physique
Note de contenu :	Sommaire Foreword ..........................................................................................................................................01 CHAPTER I :FREE OSCILLATIONS NOT DAMPED WITH ONE DEGREE OF FREEDOM ..............................5 I.1 General information on oscillations ...............................................................................................5 I.2 Degree of freedom .........................................................................................................................8 1.3 Oscillation conditions ....................................................................................................................9 I.4 Differential equation of motion ...................................................................................................10 1.4.1 Method of the fundamental principle of dynamics ..................................................................11 1.4.2 Lagrange method ......................................................................................................................13 1.5. Equation of motion (solution of the differential equation) ........................................................15 1.6. Total energy of motion ...............................................................................................................16 1.7. Equivalent systems .....................................................................................................................17 1.8. Analogy between mass-spring mechanical system (M,K) and coil-capacitor electrical system (L, C)................ Exercice............................................................................................................................................ CHAPTER II :DAMPED FREE OSCILLATIONS WITH ONE DEGREE OF FREEDOM ..................................26 II.1 Introduction ...............................................................................................................................26 II.2 Types of frictional forces ............................................................................................................26 II.3 Determining the differential equation of motion .......................................................................28 II.3.1 Method of the Fundamental Principle of Dynamics.................................................................28 II.3.2 Lagrange method .....................................................................................................................29 II.4 Determination of the equation of motion ...................................................................................31 II.5 Logarithmic decrement and quality coefficient ..........................................................................35 II.5.1 Logarithmic decrement............................................................................................................35 II.5.2 Quality coefficient ...................................................................................................................35 II.6 Analog electrical system .............................................................................................................36 Exercise ............................................................................................................................................37 CHAPTER III :DAMPED FORCED OSCILLATIONS WITH ONE DEGREE OF FREEDOM ..........................43 III.1 Introduction ...............................................................................................................................43 III.2 Differential equation of motion .................................................................................................43 III.2.1 Method of the fundamental principle of dynamics (FPD) ........................................................43 III.2.2 Lagrange method.....................................................................................................................44 III.3 Equation of motion ....................................................................................................................46 III.4 Amplitude and initial phase of steady state ...............................................................................47 III.4.1 Calculation of amplitude A ......................................................................................................48 III.4.2 Calculating the phase shift ???? : .................................................................................................49 III.5. Study of the steady state: amplitude resonance phenomenon. ................................................50 III.5.1. The variation of the amplitude as a function of the force pulsation for different values of δ.50 III.5.2. Study of resonance .................................................................................................................52 III. 5.4. Resonance phenomenon and quality factor ..........................................................................53 Exercise ............................................................................................................................................54 CHAPTER IV :N DEGREES OF FREEDOM .............................................................................................59 IV-1.Introduction ...............................................................................................................................59 IV-2. Study of a Mechanical System with N Degrees of Freedom and Fixed Ends ..............................59 IV.2.1 Derivation of the Differential Equation of Motion for Mass n .................................................59 VI.3. Study of a mechanical system with N degrees of freedom and free ends .................................62 IV.3.1. Derivation of the differential equation of motion for mass n ................................................63 IV.3.2. Derivation of the dispersion relation .....................................................................................63 Exercise :.........................................................................................................................................66 CHAPTER V : WAVES ..........................................................................................................................70 V-1 Introduction : ..............................................................................................................................70 V .2 Definition and types: ..................................................................................................................70 V.3 Progressive sinusoidal wave........................................................................................................72 V.4 Superposition of two progressive sinusoidal waves ....................................................................74 V.4.1 Case of two waves of the same frequency propagating in the same direction .........................74 V.4.2 Case of two waves of the same frequency propagating in opposite directions ........................74 V.4.3 Standing waves in a cord: .........................................................................................................76 V.5 Doppler effect: ............................................................................................................................80 Exercise : .........................................................................................................................................82 References .......................................................................................................................................84
Côte titre :	PPh/0032
En ligne :	http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/6676/1/PPH-0032.pdf
Format de la ressource électronique :	pdf

Handout Waves and vibrations ; course [texte imprimé] / Amer Saoudi . - 2026 . - 1 vol (84 p .) ; 29 cm.
Langues : Anglais (eng)

Catégories :	Publications pédagogiques:Physique P/P
Mots-clés :	Handout Waves
Index. décimale :	530-Physique
Note de contenu :	Sommaire Foreword ..........................................................................................................................................01 CHAPTER I :FREE OSCILLATIONS NOT DAMPED WITH ONE DEGREE OF FREEDOM ..............................5 I.1 General information on oscillations ...............................................................................................5 I.2 Degree of freedom .........................................................................................................................8 1.3 Oscillation conditions ....................................................................................................................9 I.4 Differential equation of motion ...................................................................................................10 1.4.1 Method of the fundamental principle of dynamics ..................................................................11 1.4.2 Lagrange method ......................................................................................................................13 1.5. Equation of motion (solution of the differential equation) ........................................................15 1.6. Total energy of motion ...............................................................................................................16 1.7. Equivalent systems .....................................................................................................................17 1.8. Analogy between mass-spring mechanical system (M,K) and coil-capacitor electrical system (L, C)................ Exercice............................................................................................................................................ CHAPTER II :DAMPED FREE OSCILLATIONS WITH ONE DEGREE OF FREEDOM ..................................26 II.1 Introduction ...............................................................................................................................26 II.2 Types of frictional forces ............................................................................................................26 II.3 Determining the differential equation of motion .......................................................................28 II.3.1 Method of the Fundamental Principle of Dynamics.................................................................28 II.3.2 Lagrange method .....................................................................................................................29 II.4 Determination of the equation of motion ...................................................................................31 II.5 Logarithmic decrement and quality coefficient ..........................................................................35 II.5.1 Logarithmic decrement............................................................................................................35 II.5.2 Quality coefficient ...................................................................................................................35 II.6 Analog electrical system .............................................................................................................36 Exercise ............................................................................................................................................37 CHAPTER III :DAMPED FORCED OSCILLATIONS WITH ONE DEGREE OF FREEDOM ..........................43 III.1 Introduction ...............................................................................................................................43 III.2 Differential equation of motion .................................................................................................43 III.2.1 Method of the fundamental principle of dynamics (FPD) ........................................................43 III.2.2 Lagrange method.....................................................................................................................44 III.3 Equation of motion ....................................................................................................................46 III.4 Amplitude and initial phase of steady state ...............................................................................47 III.4.1 Calculation of amplitude A ......................................................................................................48 III.4.2 Calculating the phase shift ???? : .................................................................................................49 III.5. Study of the steady state: amplitude resonance phenomenon. ................................................50 III.5.1. The variation of the amplitude as a function of the force pulsation for different values of δ.50 III.5.2. Study of resonance .................................................................................................................52 III. 5.4. Resonance phenomenon and quality factor ..........................................................................53 Exercise ............................................................................................................................................54 CHAPTER IV :N DEGREES OF FREEDOM .............................................................................................59 IV-1.Introduction ...............................................................................................................................59 IV-2. Study of a Mechanical System with N Degrees of Freedom and Fixed Ends ..............................59 IV.2.1 Derivation of the Differential Equation of Motion for Mass n .................................................59 VI.3. Study of a mechanical system with N degrees of freedom and free ends .................................62 IV.3.1. Derivation of the differential equation of motion for mass n ................................................63 IV.3.2. Derivation of the dispersion relation .....................................................................................63 Exercise :.........................................................................................................................................66 CHAPTER V : WAVES ..........................................................................................................................70 V-1 Introduction : ..............................................................................................................................70 V .2 Definition and types: ..................................................................................................................70 V.3 Progressive sinusoidal wave........................................................................................................72 V.4 Superposition of two progressive sinusoidal waves ....................................................................74 V.4.1 Case of two waves of the same frequency propagating in the same direction .........................74 V.4.2 Case of two waves of the same frequency propagating in opposite directions ........................74 V.4.3 Standing waves in a cord: .........................................................................................................76 V.5 Doppler effect: ............................................................................................................................80 Exercise : .........................................................................................................................................82 References .......................................................................................................................................84
Côte titre :	PPh/0032
En ligne :	http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/6676/1/PPH-0032.pdf
Format de la ressource électronique :	pdf