• Lecture 1. Introduction
• Lecture 2. Springs and Spring-Mass
• L2.1 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
• 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