Systems of first-order autonomous linear ODE, repeated roots, generalized eigenvectors
Channel: Scott Strong
Date: 10/04/2019

In this video we start with a critically damped mass-spring system, and from its re-statement in terms of a first-order system and useing the second-order ODE, derive the generalized eigenvector and explain why it should take this form. 

Link to the source files: https://www.dropbox.com/sh/vlvqqm6zxskrx41/AADFC1FFIeVCT3zbYJo48LFRa?dl=0

Table of contents: 
0:00 Introduction
0:15 Conversion to system
2:05 Solution to the second-order ODE in vector form 
3:57 Treatment of the system version w/ eigenvalue/eigenvectors 
6:48 Discussion of the second linearly independent solution
11:33 Back to the original problem
14:39 Key points in the notation used in MATH225 
16:00 Application of initial conditions and showing that either choice of generalized eigenvector was fine