PHYS 2300 - Vibrations, Waves and Optics

Index to lecture notes

PHYS 2300 notes will appear here as the course is being taught.

Lecture 2(pdf): Numbers as transformations, complex numbers, rotational motion in the vector and complex number representations, Euler Formula.

Lecture 3(pdf): Superposition of periodic motion, interference (constructive and destructive), beats.

Lecture 4(pdf): Free vibration of physical systems. Approach via conservation of energy, pendulum example. Elasticity and definitions of stress and strain. Floating objects.

Lecture 5(pdf): Free vibrations cont: Torsional pendulums via conservation of energy (including applications). Introduction of shear stress, shear modulus.

Lecture 6(pdf): Damped SHM. Resistive forces, and the resultant equation of motion. Solving using complex exponential form. Resulting equation of motion.

Lecture 7(pdf): Damped SHM cont. Energy evolution, overdamped, critically damped and underdamped solutions.

Lecture 8(pdf): Forced vibrations and resonance. Case with no damping, calculation of amplitude versus frequency. Using phase to handle negative amplitudes. Complex exponential approach to the problem.

Lecture 9(pdf): Forced vibrations with damping via the complex exponential approach. Impact of Q on the amplitude and phase of the system.

Lecture 10(pdf): Transients and reconciling steady state solutions with specified initial conditions. Evaluating amplitudes and phases for driven solutions. Beats in driven systems. Adding damping.

Lecture 11(pdf): Power in forced damped systems. Input into undamped case first, then damped case. Power usage relative to Q of system.

Lecture 12(pdf): Introduction to coupled oscillators. Examples, including the coupled pendulum case in detail. Normal modes and their application in general solutions of the equations of motion.

Lecture 13(pdf): General approach to calculating the normal mode angular frequencies.

Lecture 14(pdf): N discrete coupled oscillators with transverse oscillations. Normal modes and the separation of amplitude and time dependence.

Lecture 15(pdf): Continous systems - vibrations of a string of fixed mass per unit length. Derivation of the wave equation and solutions via trial. Overtones and allowed frequencies of stationary waves.

Lecture 16(pdf): Driven continuous systems, amplitude frequency dependence. Longitudinal vibrations in continuous systems. Impact of boundary conditions and quarter vs half wavelength modes.

Lecture 17(pdf): Brief introduction to Fourier series. Fourier series in space and time. Evaluating constants in the series expansion of a function.

Lecture 18(pdf): Travelling waves. Expansion of a standing wave into two travelling waves. Equation of motion. Superposition of waves and pulses.

Lecture 19(pdf): Superposition of travelling waves: energy and dispersion. Phase and group velocities.

Lecture 20(pdf): Energy in a wave: evaluation of kinetic and potential pieces, plus power associated with setting up the wave.

Lecture 21(pdf): Boundary and interference effects. Handling discontinuities, evaluating the reflected and transmitted parts of the wave. Testing against fixed, free and no end conditions.

Lecture 22(pdf): Huygens-Fresnel Principle. Reflection and refraction formulae. Doppler effect.

Lecture 23(pdf): Huygens-Fresnel Principle applied to double-slit and diffraction gratings.