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Fundamentals of Dynamics and Oscillations
Rating: 5.0 out of 5(4 ratings)
14 students

Fundamentals of Dynamics and Oscillations

Build a solid foundation in mechanical vibrations through step-by-step modeling, analysis, and guided problem solving
Created byDavid Dimitrov | SimX Academy
Last updated 4/2026
English

What you'll learn

  • Model linear mechanical rigid-body 1-DOF systems using the impulse and angular-momentum theorem
  • Derive equations of motion systematically from physical principles
  • Analyze undamped and damped oscillations and interpret their physical meaning
  • Determine eigenvalues and derive homogeneous solutions of linear differential equations
  • Solve harmonic and periodic excitations in the frequency domain using Laplace transforms and transfer functions
  • Analyze arbitrary excitations using impulse response functions and the convolution integral
  • Develop confidence in interpreting vibration behavior of mechanical systems
  • Apply dynamics concepts reliably instead of relying on memorized formulas or procedural guessing

Course content

8 sections • 30 lectures • 4h 22m total length

  • What you will learn1:40
  • Preview Exercise 1: Laser pendulum cutting process7:58
  • Preview Exercise 2: Periodically excited conveyor belt3:36
  • Preview Exercise 3: Car on a bumpy road2:35

Requirements

  • Basic calculus & Complex numbers & Trigonometry
  • Linear ordinary differential equations basics
  • You should have heard of the Laplace Transformation and Fourier Series
  • Fundamental mechanical concepts: mass, inertia, simple mechanical elements
  • No programming or software knowledge is required
  • More important than prior knowledge is your willingness to think quantitatively and to engage deeply with the material
  • All concepts are developed step by step and any required theory is introduced exactly where it is needed—no prior specialization in vibrations or dynamics is assumed

Description

This course is for you if:

  • You want to truly understand vibrations, not just apply formulas 

  • You prefer structured, step-by-step learning   

  • You enjoy solving guided exercises from real-world engineering 

  • You are willing to actively work through problems and think quantitatively 


This course is designed for engineering students, early-career engineers, and practitioners who want to understand dynamics and oscillations properly—not just apply formulas mechanically or rely on memorized procedures

With a high-information density, you will learn how linear mechanical 1-degree-of-freedom systems are modeled from first principles, how their equations of motion are derived systematically, and how their dynamic behavior can be analyzed and interpreted with confidence.

Instead of overwhelming you with abstract theory, each concept is introduced only as deep as necessary, then applied directly to engineering-relevant examples. Every topic follows a logical sequence, building step by step from undamped systems to damped motion, harmonic and periodic excitation, and finally arbitrary excitations using the convolution integral.

A strong emphasis is placed on guided exercises. You will not just watch derivations—you will actively work through problems, develop intuition for vibrations, and learn how to interpret system behavior in a way that transfers directly to real engineering tasks. The concepts developed in this course form the theoretical foundation for highly relevant industry fields such as Noise Vibration and Harshness (NVH) analysis in the automotive sector and rotor dynamics in turbomachinery and high-speed rotating equipment. Understanding single-degree-of-freedom vibration systems is the essential first step toward mastering these advanced applications.

By the end of this course, you will no longer rely on inserting memorized formulas or performing trial-and-error calculations. You will be able to analyze and solve vibration problems in mechanical engineering with confidence and structure.

Who this course is for:

  • Mechanical engineering students and related fields (e.g. mechatronics, industrial engineering)
  • Engineering students struggling with dynamics and vibrations
  • Early-career engineers who want a deeper, more reliable understanding of oscillations
  • Engineers who want to strengthen their theoretical foundation to work more confidently in practice

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