Part I: Oscillations
Oscillatory motion is one of the most ubiquitous phenomena in physics. From the swinging of a pendulum to the vibrations of atoms in a crystal lattice, oscillations form the conceptual bridge between discrete particle mechanics and the continuous wave phenomena explored later in this course.
Part Overview
We begin with the simple harmonic oscillator, the most fundamental oscillatory system, and progressively add complexity: damping, driving forces, and coupling between oscillators. The continuum limit of coupled oscillators leads naturally to the wave equation, bridging Parts I and II.
Key Topics
- \(\bullet\) Simple harmonic motion: \(x = A\cos(\omega t + \phi)\)
- \(\bullet\) Energy in oscillatory systems: kinetic and potential energy exchange
- \(\bullet\) Damped oscillations: underdamped, critically damped, overdamped
- \(\bullet\) Forced oscillations and resonance phenomena
- \(\bullet\) Coupled oscillators: normal modes and beating
- \(\bullet\) Dispersion relations and the continuum limit
- \(\bullet\) LC circuits as electrical oscillators
3 chapters | Foundation for wave mechanics | Bridges to EM waves and optics
Chapters
Chapter 1: The Harmonic Oscillator
Simple harmonic motion, energy conservation, the spring-mass system, the simple pendulum, LC circuits, and complex notation for oscillations.
Chapter 2: Damped & Driven Oscillators
Damping regimes (underdamped, critical, overdamped), quality factor, forced oscillations, resonance curves, transient and steady-state response.
Chapter 3: Coupled Oscillators
Normal modes, beating, N-coupled oscillators, dispersion relation, and the continuum limit leading to the wave equation.