Calculus 2, Lec 35A, Harmonic Oscillator System Phase Portrait (Phase Plane) on Mathematica

Calculus 2, Lecture 35B. Use Mathematica to make the phase portrait of a harmonic oscillator model with damping.

(0:00) Mathematica notebook and lecture plans.
(1:33) Harmonic oscillator with friction ("damping").
(9:14) Find solution to various initial value problem to the single second-order (scalar) equation with DSolveValue in Mathematica.
(14:16) Corresponding system of two first-order equations.
(16:10) Find the solution to the second order system with DSolveValue in Mathematica.
(19:42) Use ParametricPlot and Manipulate to plot the solution curve in the phase plane.
(26:09) Add the vector field to the phase plane with VectorPlot.
(31:19) Description of what it means for a solution curve to "follow" a vector field, as well as how the vector field and the corresponding direction field are constructed.
(34:16) Continue making the picture prettier and more relevant (and include a dot at the equilibrium point at the origin).