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Mechanical Vibrations (+88 Solved Examples + MATLAB)

Name: Mechanical Vibrations (+88 Solved Examples + MATLAB)
Rating: 4.5 (41 reviews)

Mechanical Vibrations: Detailed Explanations + Many Detailed Solved Examples + MATLAB

Created byMahdy Eslamy, PhD

Last updated 6/2026

English

What you'll learn

1. Introduction and Basic Definitions
2. Modelling of Dynamical Vibratory Systems
3. Free Vibration of Undamped Systems
4. Free Vibration of Damped Systems
5. Forced Vibrations (Damped & Undamped Systems)
6. Analysis of Two-DoF Systems
7. Many Solved Examples in Each Chapter
8. Learn How to Use Matlab to Solve Vibration Equations

Course content

7 sections • 129 lectures • 16h 8m total length

Welcome Video and Course Introduction1:27
In this section you get familiar with me as the lecturer and also get familiar about the goals of this course.

2.1. Basic Definitions and Requirements1:37
2.2. Modelling11:33
2.2. Modeling: Important Points for Modeling of Dynamical Vibratory Systems5:48
2.2. Modeling: Important Points - part 24:24
Explains how to derive the equation of motion using the Lagrange-Euler method and the energy method, detailing kinetic energy, potential energy, dissipative energy, nonconservative forces, and time derivatives.
2.2. Modeling: Important Points - part 32:23
2.2. Modeling: Important Points - part 43:08
2.2. Warm-up Example 19:31
2.2. Warm-up Example 25:45
2.2. Warm-up Example 313:37
2.2. Warm-up Example 3 - Important Point3:10
2.2. Warm-up Example 412:05
2.2. Warm-up Example 511:17
2.2. Warm-up Example 69:40
2.2. Warm-up Example 714:22
2.2. Warm-up Example 89:23
2.2 Example 110:50
2.2. Example 27:38
2.3. Equivalent Systems1:46
2.3 Example 315:18
2.3 Example 49:55
2.3 Example 53:23
2.3 Example 65:01
2.4 Gravity Force Cancellation1:59
2.4 Example 74:42
2.4 Example 83:53
2.4 Example 98:43
2.5: Natural Frequency3:07
2.5 Example 101:58
2.6 Further Examples Example 117:43
2.6 Further Examples Example 127:17
2.6 Further Examples Example 1316:59
2.6 Further Examples Example 1411:35
2.6 Further Examples Example 155:04
2.6 Further Examples Example 169:07
2.6 Further Examples Example 177:10
2.6 Further Examples Example 186:20
2.6 Further Examples Example 198:00
2.6 Further Examples Example 207:29
2.6 Further Examples Example 214:19
Derive the equation of motion for a small-cylinder spring-mass system using x dot = r theta dot and kinetic energy. Find the natural frequency omega_n = sqrt(2k/(3m)).
2.6 Further Examples Example 228:22
2.6 Further Examples Example 234:56
2.6 Further Examples Example 244:26
2.6 Further Examples Example 255:24
2.6 Further Examples Example 268:17
2.6 Further Examples Example 279:50
2.6 Further Examples Example 287:26
2.6 Further Examples Example 298:20
2.6 Further Examples Example 308:33
2.6 Further Examples Example 312:19
2.6. Further Examples Example 3227:22
2.6. Further Examples Example 3314:00
2.6. Further Examples Example 3416:44
2.6. Further Examples Example 3513:10
Derive the equation of motion for the mass m with three springs in series and massless pulleys using equivalent springs, as shown in example 2.35, and demonstrate multiple solution approaches.
2.6. Further Examples Example 3613:45
2.6. Further Examples Example 3710:43
Derive the equation of motion using the Newton-Euler method for a one-degree-of-freedom rod-mass system with gravity and a torsional spring, and determine the natural frequency from equivalent stiffness and mass.
2.7. Equivalent Torsional Stiffness (using Mechanics of Materials)6:52
2.8. Equivalent Bending Stiffness (using Mechanics of Materials)5:49
Chapter 2 Summary1:37

3.1. Basic Definitions4:37
3.2. Solving Diff. Eq. of Free Undamped Systems5:21
3.2. Example 15:37
3.3 Solving Diff. Eq. using Matlab Example 27:11
3.4. Mechanical Energy of Free Undamped Systems4:39
3.5. Maximum Kinetic vs. Maximum Potential Energy of Free Undamped Systems4:26
3.6. When Do We Have Max Kinetic and Max Potential Energy in Free Undamped Sys6:40
3.7. Phase Plane Analysis of Free Undamped Systems5:00
3.8. Examples Example 313:07
3.8. Examples Example 47:50
3.8. Examples Example 50:45
3.8. Examples Example 625:40
3.8. Examples Example 727:42
3.8. Examples Example 814:58
3.8. Examples Example 914:11
3.8. Examples Example 107:57
Chapter 3 Summary2:24

4.1. Basic Definitions2:44
4.2. Solving Diff. Equation of Free Damped Systems15:45
4.3. Under-damped Oscillatory Motion4:43
4.4. Logarithmic Decrement8:43
4.5 Examples Example 16:30
4.5 Examples Example 26:08
4.5 Examples Example 34:49
4.5 Examples Example 3 - Second Way6:36
Demonstrates solving the equation of motion in Matlab with ode45 by converting to two first-order equations, x1 = x and x2 = x dot, and solving 0 to 6 seconds.
4.6 Phase Plane Analysis of Free Damped Sys. Examples 4 to 63:52
4.7. Stability of Free Damped Systems3:59
4.8. Examples Example 78:10
4.8. Examples Example 81:53
4.8. Examples Example 99:15
4.8. Examples Example 1021:35
4.8. Examples Example 10-16:15
4.8. Examples Example 1112:01
4.8. Examples Example 1210:28
Chapter 4 Summary2:49

5.1. Basic Definitions1:55
Explain forced vibrations by introducing external excitation and contrast them with free vibrations, using m x'' + c x' + k x = f(t) to show how f(t) drives motion.
5.1: Basic Definitions Example 11:27
5.2. Solving Diff. Equation of Forced Vibrations3:38
5.3. Harmonic Excitation9:32
5.4. Magnification Factor (Amplitude Ratio)6:12
Define the magnification factor beta as a dimensionless amplitude ratio; show how beta increases with lower damping and certain frequency ratios, and how damping prevents unbounded amplification.
5.4. Magnification Factor Example 22:54
5.5. Resonance4:46
5.6. Examples Example 38:40
5.6. Examples Example 44:36
5.6. Examples Example 53:18
5.6. Examples Example 67:32
5.6. Examples Example 78:26
5.6. Examples Example 87:37
5.6. Examples Example 9 - Coulomb Friction - part 113:11
5.6. Examples Example 9 - part 27:43
5.6. Examples Example 10 - Coulomb Friction4:33
5.6. Examples Example 11 - Road Surface - part 17:44
5.6. Examples Example 11 - Road Surface - part 25:21
5.6. Examples Example 12 - Road Surface & Damping Effects17:36
5.7. Rotating Unbalance10:01
Chapter 5 Summary3:49

6.1. Basic Definitions2:40
6.2. Obtaining the Equations of Motion (EoM) of a 2-DoF System1:04
Derive the equations of motion for a two-dimensional system by applying the Newton–Euler or energy method, and define two independent variables to fully specify its equation of motion.
6.3. Examples Example 15:08
6.3. Examples Example 23:59
6.3. Examples Example 36:30
6.3. Examples Example 44:43
6.3. Examples Example 57:51
6.4. Writing Equations of Motion in Matrix Form4:19
6.5. Obtaining the Natural Frequency of a 2-DoF system4:17
6.6. Examples Example 62:49
6.7. Motion Analysis of 2-DoF Systems1:25
6.8. Examples Example 78:54

Requirements

Please be familiar with Dynamics, Differential Equations, and Calculus

Description

Hi!

I hope you are doing great!

Would you like to familiarize yourself with, and strengthen your knowledge about Mechanical Vibrations and motion analysis of mechanical systems? Then, This Course Is For You, Welcome on Board!

Mechanical Vibration is one the most important and fundamental courses of mechanical engineering. During this course, you will learn how to analyze the motion of different vibratory systems. You will learn the impact and importance of selecting reasonable mass, spring and damping, in order to guarantee a logical motion for a mechanical system. This course paves the way to prepare you for mechanical engineering design.

The course is therefore composed of the following chapters:

Chapter 1: Introduction and Basic Definitions
Chapter 2: Modelling of Dynamical Vibratory Systems
Chapter 3: Free Vibration of Undamped Systems
Chapter 4: Free Vibration of Damped Systems
Chapter 5: Forced Vibrations
Chapter 6: Analysis of Two-DoF Systems

In addition, it includes:

Many Solved Examples in Each Chapter
High Quality Pictures
High Quality Videos
Detailed Explanations
You Learn By Solving Relevant Up-to-date Examples
Summary and Review Covered at the End of Each Chapter
Very Clear English, Any Student Can Comprehend the Topic
You Learn How to Combine this Course with MATLAB to Maximize Your Expertise. Different Examples are Solved Using MATLAB.

This course is designed very carefully for the students of mechanical engineering, and people who are interested to learn what mechanical vibration is. It guides you from the first elementary step through to the expertise level in this field.

I am sure after passing this course you feel very confident not only in mechanical vibrations, but also in dynamics and differential equations in MATLAB.

This course can even be used by the students who want to deepen their knowledge in Dynamics, and evaluate how they can combine it with Matlab. You can even combine this course with what you learn in control engineering to investigate how to modulate the motion of mechanical systems. Furthermore, the course is updated regularly to contain as much information as possible.

Mechanical Vibrations Course

Mechanical Vibrations,

Detailed Explanations,

Many Solved Examples,

MATLAB,

Vibration,

Equations of Motion,

Dynamics Analysis,

Degrees of Freedom,

Vibrations

Who this course is for:

This course is designed very carefully for the students of mechanical engineering, and people who are interested to learn what mechanical vibration is.

Mechanical Vibrations (+88 Solved Examples + MATLAB)

What you'll learn

Explore related topics

Course content

Course Introduction1 lecture • 1min

Chapter 1: Introduction and Basic Definitions2 lectures • 13min

Chapter 2: Modelling of Dynamical Vibratory Systems58 lectures • 7hr 45min

Chapter 3: Free Vibration of Undamped Systems17 lectures • 2hr 38min

Chapter 4: Free Vibration of Damped Systems18 lectures • 2hr 16min

Chapter 5: Forced Vibrations (Damped & Undamped Systems)21 lectures • 2hr 21min

Chapter 6: Analysis of 2-DoF systems12 lectures • 54min

Requirements

Description

Who this course is for: