ABSTRACT
This chapter discusses the problem of harmonic motion. It first introduces general concepts of linear ordinary differential equations and presents the simplest application of these equations for a linear harmonic oscillator, with and without damping forces. This is followed by the study of forced or driven oscillations under an external force, and the important concepts of amplitude resonance, energy resonance, and the associated Q-factor for oscillatory systems. Simple harmonic motion occurs when an object displaced a small distance from a stable equilibrium experiences a restoring force towards the equilibrium state. An important example of simple harmonic motion is a mass attached to a massless spring with no friction. The quality factor is a dimensionless parameter that quantifies the degree of damping present in an oscillator. The chapter concludes by introducing the physical concepts of phase space and the superposition principle, together with the important mathematical technique of Fourier analysis.
