Textbook of Waves and Vibration

1.    Simple Harmonic Motion
2.    Damped Harmonic Oscillator
3.    The Forced Oscillator
 

• Oscillatory motion: Simple harmonic motion (SHM), damped oscillations (underdamped/overdamped), forced oscillations and resonance.

• Coupled oscillators and normal modes: systems of masses and springs, continuous systems, etc.

• Wave motion: travelling waves, standing waves, longitudinal and transverse waves.

• Wave properties: speed, frequency, wavelength, superposition, interference, beats.

• Boundary conditions, reflection & transmission at boundaries or discontinuities.

• Dispersion, phase & group velocity.

• Fourier methods: how to describe general oscillations/waves via superposition of simpler ones.

• Applications: mechanical waves (strings, rods, membranes), sound waves, sometimes electromagnetic waves; possibly more advanced topics like solitons, wave mechanics.