- Lecture 1. Introduction
- Lecture 2. Springs and Spring-Mass
- L2.1 springs [video]
- L2.2 adding springs [video]
- L2.3 spring-mass system [video]
- Lecture 3. Solving second order differential equation (integrating factor method)
- L3.1 solving 1st order differential equation [video]
- L3.2 properties of exponential [video]
- L3.3 properties of logarithm [video]
- L3.4 connection between exponential, sine, cosine [video]
- L3.5 solving the 2nd order homogeneous equation [video]
- Lecture 4. Damped Vibrations
- L4.1 adding damping to the problem [video] [pdf]
- L4.2 integrating factor [video] [pdf]
- L4.3 solving the damped differential equation [video] [pdf]
- L4.4 grinding some algebra [video] [pdf]
- L4.5 phase shift [video] [pdf]
- L4.6 using the formula to solve some problems (requires python) [video] [code]
- Lecture 5: Forced Vibrations
- Integrating factor method
- L5.1 [video] and notes [PDF] (integrating factor for 2nd order damped)
- L5.2 [video] and notes [PDF] (checking the solution)
- L5.3 [video] and notes [PDF] (making it real)
- L5.4 [part one – video][part two – video] and notes [PDF] (making it more real)
- L5.5 [video] (python-ing the expression) [python code]
- Homogeneous and Particular solution method
Chapter 2 lecture notes (PDF)
- Lecture 6: Ground motion (base excitation)
- L6.1 Base Excitation. setting up the forcing function [video]
- L6.2 solving the differential equation [ video]
- L6.3 Finalizing the solution. Matching initial conditions, Displacement transmissibility [ video]
- L6.4 Force transmissibility [ video]
- Lecture 7: Rotating unbalance
- Lecture 8: Vibration suppression
- L8.1 Setting up the problem [video]
- L8.2 Review of amplitude ratio
- L8.3 Force ratio revisited
- L8.4 RMS and Nomograph
- L8.5 Example of vibration isolation (material selection)
- L8.6 Simple vibration absorber (derivation)
- L8.7 Vibration absorber example
- Lecture 9: Vibration analysis using python
