Explore advanced concepts in harmonic motion and waves in this comprehensive physics lecture from Yale University. Delve into free vibration, initial conditions of oscillation, and solutions to harmonic equations under driving forces. Examine the properties of oscillating functions and the phenomenon of resonance. Learn about complementary and particular solutions before transitioning to an introduction on waves. Distinguish between longitudinal and transverse waves, derive the wave equation as a differential equation, and discover its solutions. Gain a deeper understanding of fundamental physics principles through this 75-minute lecture, which is part of a larger course on mechanics, relativity, and thermodynamics.