Characteristics of Oscillations

This lecture covers the concept of characteristic times in physics and engineering, where systems are analyzed using reduced coordinates. The instructor explains how these timescales can vary from seconds to nanoseconds, yet the same equations can model different systems. Examples include harmonic oscillators in bridges, buildings, and even high towers like the Taipei 101. The lecture also delves into differential equations, focusing on linear first and second-order equations, and the different types of solutions they yield. The importance of neglecting terms in calculations is emphasized, with practical examples such as GPS systems and rifle dynamics. Students are guided on how to determine when a term can be neglected and the implications of such approximations.