8.03 Lectures - Fall 1997

L1 - Sep. 3

Introduction, course organization, policies, etc.
Preview of Weeks 1-6
DEMOs: mass on spring, 2 identical pendulums with different amplitudes, 2 weakly coupled pendulums, Bell Labs wave machine, Chladni figures on square plate (speaker driven)

L2 - Sep. 5

Simple harmonic oscillations - definitions and notations
Rotating vector representation
Complex exponential representation
DEMOS: oscillations of spray paint can, vertical oscillations of mass on spring vs projected circular motion

L3 - Sep. 8

Superposition of two SHO's with same amplitude and frequency (interference)
Superposition of two SHO's with same amplitude and different frequencies (beats)
PLOTS: beats
DEMOS: two speakers (in phase/ out of phase), two tuning forks (beats)

L4 - Sep. 10

Equation of motion of SHO without damping - mass on spring
Damping (fluid viscosity, dry friction, aerodynamic drag, electromagnetic damping)
Motion of SHO with damping (light damping, critical damping, heavy damping, Q factor)
DEMOs: cart between springs on an air track, copper plate moved across strong magnet, torsional oscillator with electromagnetic damping, two masses on springs with different dampings

L5 - Sep. 12

Examples of SHO's
Vertical oscillations of floating objects
The energy method
Oscillations of the water in a U-shaped tube
Pendulums (torsional oscillations of a solid body)
DEMOs: slinky, longitudinal vibrations of copper and manganese bars, bouncing balls, bobbing float, water in U-shaped tube, physical pendulum, ball on circular track

L6 - Sep. 15

Complex impedance of an electrical circuit
Complex impedance of the series RLC circuit - Resonance
DEMOs: damped free oscillations of RLC circuit, driven oscillations of RLC circuit (connected to speaker), maximizing dissipation at resonance in RLC circuit (with light bulb)

L7 - Sep. 17

Driven RLC circuit: current amplitude, phase, power absorbed
PLOTS: current amplitude and phase vs frequency for various values of Q
Comparison between driven RLC circuit and driven mechanical oscillator, mechanical impedance
HANDOUT: summary of results for driven RLC circuit and driven mechanical oscillator.
DEMOs: mass on spring driven by hand (stiffness-, mass-, damping-controlled limits), resonance and transients (on/off resonance) for driven cart on air track
Transients - General solution of driven oscillator equation

L8 - Sep 19

More examples of resonances (electrical circuits, acoustic, spectra, astrophysics, etc.)
DEMOs: resonance in LC circuit driven by mutual inductance, frequency sweep of RLC circuit, Helmholtz resonator, resonance between two tuning forks (on/off resonance)
PLOTS: various resonance curves
Intro to Fourier series: general periodic forcing and Fourier analysis in the time domain
HANDOUT: Fourier analysis in the time domain
VIDEO: collapse of the Tacoma Narrows Bridge

L9 - Sep 24

Harmonic oscillator in 2 dimensions
Two coupled oscillators - general method, normal modes
General solution as superposition of normal modes
DEMOs: two strongly coupled (by rod) pendulums, two weakly coupled rigid pendulums, Wilberforce pendulum, loaded hacksaw blade

L10 - Sep 26

Longitudinal oscillations of masses coupled by springs
Normal modes and normal coordinates
Forced vibrations of coupled systems
DEMO: normal modes of 5 carts coupled by springs on air track

L11 - Sep 29

Derivation of the wave equation for transverse vibrations of a string under tension
Normal modes for vibrating string fixed at both ends
DEMO: normal modes of a long spring/ slinky

L12 - Oct 1

Boundary conditions: free vs fixed ends
Initial conditions for vibrating string
General solution as an infinite series of normal modes
Fourier coefficients for given initial shape
DEMOs: modes of Bell Labs wave machine (both ends free),

L13 - Oct 3

Fourier series and normal modes
Physics of musical instruments: timbre vs pitch, harmonics, octaves, fifths
Wave equation for longitudinal sound waves in pipes
Normal modes for pipe open at both ends
DEMOs: standing sound waves in plexiglas tube driven by speaker (both ends closed), guitar, violin, tuba

L14 - Oct 6

Review for Quiz 1 (F. Rasio)

L15 - Oct 8

QUIZ 1

L16 - Oct 10

Guest lecture by Walter Lewin: The Physics of Sound

L17 - Oct 15

Traveling waves
Standing waves (normal modes) as superposition of traveling sine waves
DEMOs: longitudinal wave pulses on long spring, Bell Labs wave machine (pulse propagation, reflection), addition of sine waves to give standing waves

L18 - Oct 17

Wave pulses, superposition
Reflection at a fixed boundary
Solution of the wave equation in terms of traveling waves for a stationary initial condition
DEMOs: stationary initial condition on the Bell Labs wave machine, wave pulses on a spinning chain

L19 - Oct 20

Electrical and mechanical transmission lines
Derivation of the wave equation for voltage and current
Capacitance and inductance per unit length, speed of propagation
Traveling waves generated at one end, retarded time
DEMOs: pulse propagation and reflection on a coaxial cable, microwave propagation in parallel plate line

L20 - Oct 22

Traveling sinusoidal waves for voltage and current
Characteristic impedance of a transmission line
DEMO: coaxial cable terminated on its characteristic impedance
Coaxial cable: calculation of the inductance and capacitance per unit length
Reflection at a purely resistive load, voltage and current reflection coefficients

L21 - Oct 24

Reflection for complex load impedance, complex reflection coefficient
Reflection/transmission at boundary between two lines of different charateristic impedances
Power transmitted by a sinusoidal traveling wave, energy conservation at a boundary
Characteristic mechanical impedance of a vibrating string
Standing waves on a short-circuited or open transmission line
Input impedance of a short-circuited transmission line
DEMOs: Bell Labs wave machine correctly terminated on a damper, reflection between two sections/tapered section, standing waves on Lecher lines

L22 - Oct 27

DEMO: propagation of EM waves, polarization (using linear antennas), microwaves (E-field probe, standing waves), disassembled microwave oven
Plane waves and the wave equation in 3-D
Derivation of the wave equations for E and B from Maxwell's equations in vacuum
EM waves in transmission lines

L23 - Oct 29

Properties of EM plane waves in vacuum
Force on a charged particle from an EM wave
Energy conservation in E&M: Poynting's theorem
Energy density and energy flux in EM plane waves
Intensity, orders of magnitudes for various sources of radiation

L24 - Oct 31

Linear, elliptical and circular polarization
Polarizers, Malus' Law
DEMOs: linear polarization of microwaves (polarizer and speaker), linear polarization of light (2 and 3 polarizers on overhead projector), circular polarization of transverse waves on long spring.

L25 - Nov 3

EM wave front emitted by a briefly accelerated charge (propagating kinks in field lines)
E and B fields of an accelerated charge
Energy flux, radiation pattern for constant acceleration
Total power radiated by an accelerated charge, the Larmor formula
Video: time-dependent field lines around accelerated charges (stopping and starting, SHM, circular motion)

L26 - Nov 5 (given by Prof. Schechter)

Cyclotron radiation (circular motion of a charged particle in a constant magnetic field, power emitted, polarization of cyclotron radiation)
Linear antennas, radiation pattern and radiation resistance for half-wave antenna
DEMO: AM broadcasting and reception with short linear antennas
HANDOUT: EM wave emission from accelerated charges (SHM in 1-D, circular motion)

L27 - Nov 7

DEMO: scattering of light by water - polarization of scattered light
Classical model of atomic vibrations, radiation damping
Scattering by atoms, scattering cross section
Rayleigh, Thomson, and resonant scattering
Examples: solar corona, blue sky, red sunsets
DEMO: sunset on a desert island with palm tree, scattering of light by cigar smoke

L28 - Nov 12

Review for Quiz 2 (M. Chen)

L29 - Nov 14

QUIZ 2

L30 - Nov 17

Reflection and refraction in geometrical optics, critical angle for total internal reflection
Speed of propagation in a dielectric, index of refraction
Snell's law from boundary conditions, wavefront continuity
DEMOs: reflection and refraction of laser beam at water-air interface, total internal reflection, optical wave guides and fibers

L31 - Nov 19

Reflection and transmission at normal incidence on a perfect dielectric
Reflection and refraction at oblique incidence, Fresnel relations
Polarization of reflected light, Brewster's angle
DEMOs: Brewster angle at air-glass interface, looking at reflected light through a polarizer

L32 - Nov 21

Microscopic picture of reflection and refraction, Huygens' principle
Microscopic explanation of Brewster's angle
Total internal reflection and evanescent waves
Frustrated total internal reflection, beam splitter
DEMO: beam splitter

L33 - Nov 24

Two beam interference - intensity vs phase
Intererence between two antennas driven in or out of phase
DEMOs: interference between two point sources in ripple tank, interference between two microwave emitters

L34 - Nov 26

DEMOs: lots of soap bubbles, air gap between optical flats, reflection from soap film, reflected light from coated lens
Thin film interference
Green and magenta: the colors of soap films and oil spills
Normal modes of rectangular membrane
VIDEO: normal modes of soap films

L35 - Dec 1

Interference from a linear array of N antennas
Reflection and refraction at the surface of a dielectric as an interference process
N sources of light - diffraction gratings
DEMOs: transmission grating with laser, looking at various sources through diffraction gratings

L36 - Dec 3

Radiation patterns from N sources
PLOTs: radiation patterns (PDF).
Diffraction by a narrow slit in 1-D
DEMO: diffraction by a single slit with laser

L37 - Dec 5

Diffraction vs Interference pattern from diffraction gratings - missing orders
Diffraction by a rectangular aperture
Diffraction by a circular aperture
Diffraction-limited beams
DEMOs: diffraction of laser light by circular pinhole, diffraction of plane waves by slit in ripple tank

L38 - Dec 8

Review for Quiz 3 (V. Kaspi)

L39 - Dec 10

QUIZ 3

8.03 Lectures - Fall 1997 - rasio@mit.edu