Explore the intricacies of damped harmonic oscillators in this 37-minute video tutorial. Delve into plotting position vs. time and phase space for both over-damped and under-damped scenarios, incorporating initial conditions. Begin with a comprehensive review of the solution, then progress to determining initial conditions for over-damped systems. Learn to plot over-damped oscillations and compare them with numerical solutions. Transition to under-damped systems, examining their initial conditions and plotting techniques. Access supplementary resources, including a derivation video and code samples for both over-damped and under-damped plots. Note: An error in the original under-damped plot code has been corrected and updated.