Differential Equations: Oscillatory Motion

This lecture covers the topic of differential equations applied to oscillatory motion, including cases with and without friction. The instructor explains the solutions to the differential equations and the behavior of the system in different scenarios, such as critically damped, underdamped, and overdamped. The lecture also delves into the concept of characteristic polynomials and the influence of initial conditions on the motion. Various methods for finding particular solutions are discussed, such as Ansatz and Variation of Parameters. The presentation concludes with a detailed analysis of the oscillatory behavior in different damping regimes.