Objective(s):
To develop a unified mathematical theory of oscillations and waves in physical systems.
Simple and Damped Simple Harmonic Oscillation:
Mass-Spring System, Simple Harmonic Oscillator Equation, Complex Number Notation, LC Circuit, Simple Pendulum, Quality Factor, LCR Circuit.
Forced Damped Harmonic Oscillation:
Steady-State Behavior, Driven LCR Circuit, Transient Oscillator Response, Resonance.
Coupled Oscillations:
Two Spring-Coupled Masses, Two Coupled LC Circuits, Three Spring Coupled Masses, Normal Modes, Atomic and Lattice Vibrations.
Transverse Waves:
Transverse Standing Waves, Normal Modes, General Time Evolution of a Uniform String, Phase velocity, Group Velocity.
Longitudinal Waves:
Spring Coupled Masses, Sound Waves in an Elastic Solid, Sound Waves in an Ideal Gas.
Traveling Waves:
Standing Waves in a Finite Continuous Medium, Traveling Waves in an Infinite Continuous Medium, Energy Conservation, Transmission Lines, Reflection and Transmission at Boundaries, Electromagnetic Waves.
Wave Pulses:
Fourier Series and Fourier Transforms, Bandwidth, Heisenberg’s Uncertainty Principle.
Multi-Dimensional Waves:
Plane Waves, Three-Dimensional Wave Equation, Laws of Geometric Optics, Waveguides, Cylindrical Waves.
Interference and Diffraction of Waves:
Double-Slit Interference, Single-Slit Diffraction.