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.