Harmonic Oscillations: Definition

This lecture introduces harmonic oscillations, defined as functions of the form f: R → R, t → f(t) = A sin(wt + p) or f: R → R, t → f(t) = A cos(wt + p), where A is the amplitude and p is the phase. The concept is illustrated through the example of uniform circular motion, where the projection of a point M on the y-axis results in an oscillation of the form A sin(wt + y), and on the x-axis as A cos(wt + p). The lecture covers the properties of harmonic oscillations and their geometric interpretation, setting the stage for the principle of superposition and practical applications.