8.03 Lectures - Spring 1998

L1 - Wed, Feb 4

• Introduction, course organization, policies, etc.
• Examples of Simple Harmonic Oscillations: mass on spring, simple pendulum
• Preview of first half of the course
• DEMOs: mass on spring, 2 weakly coupled pendulums, Bell Labs wave machine, Chladni figures on square plate (speaker driven), breaking glass

L2 - Mon, Feb 9

• More examples of SHOs: LC circuits, vertical oscillations of floating objects, oscillations of the water in a U-shaped tube, general pendulum
• The energy method
• Rotating vector representation
• Complex exponential representation
• DEMOs: bobbing float, water in U-shaped tube, physical pendulum, ball on circular track, rocking horse, vertical oscillations of mass on spring vs projected circular motion two speakers (in phase/ out of phase)
• Superposition of two SHO's with same amplitude and frequency (interference)

L3 - Wed, Feb 11

• Superposition of two SHO's with same amplitude and different frequencies (beats)
• Damping (fluid viscosity, dry friction, aerodynamic drag, electromagnetic damping)
• Motion of SHO with damping (light damping, critical damping, heavy damping)
• DEMOs: two tuning forks (beats), 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, bouncing balls

L4 - Tuesday, Feb 17

• Complex impedance of an electrical circuit
• Combining impedances in series and in parallel
• Average power absorbed
• Complex impedance of the series RLC circuit - Resonance
• DEMOs: forced oscillations of mass on spring and pendulum, driven oscillations of RLC circuit (connected to speaker), maximizing dissipation at resonance in RLC circuit (with light bulb)

L5 - Wed, Feb 18

• Driven RLC circuit: current amplitude, phase, power absorbed
• The Q factor of an oscillator - examples
• PLOTS: current amplitude, phase and power absorbed vs frequency for various values of Q
• Comparison between driven RLC circuit and driven mechanical oscillator, mechanical impedance
• DEMOs: mass on spring driven by hand (stiffness-, mass-, damping-controlled limits), resonance for driven cart on air track, frequency sweep of RLC circuit, Helmholtz resonator, resonance between two tuning forks (on/off resonance)
• VIDEO: collapse of the Tacoma Narrows Bridge

L6 - Mon, Feb 23

• Transients - General solution of driven oscillator equation
• DEMO: transients (on/off resonance) for driven cart on air track
• Intro to coupled oscillations
• Harmonic oscillator in 2 dimensions
• DEMOs: two strongly coupled (by rod) pendulums, two weakly coupled rigid pendulums, Wilberforce pendulum, loaded hacksaw blade

L7 - Wed, Feb 25

• Two coupled oscillators - general method, normal modes
• General solution as superposition of normal modes
• Three masses coupled by springs
• DEMO: normal modes of 3 carts coupled by springs on air track

L8 - Mon, March 2

• Derivation of the wave equation for transverse vibrations of a string under tension
• Speed of propagation for string under tension
• Normal modes for vibrating string fixed at both ends
• Wave number, wavelength, harmonics
• DEMO: normal modes of a long spring, driven modes of string with strobes

L9 - Wed, March 4

• Harmonics and music: timbre vs pitch, octaves, fifths
• Physics of string instruments
• Initial conditions for vibrating string
• General solution as an infinite series of normal modes
• DEMOs: playing the violin, harmonics on the violin, guitar, waveforms produced by various musical instruments, timbre vs pitch with clarinet and flute

L10 - Mon, March 9

• Traveling waves
• Forced motion and retarded time
• Normal modes as superposition of traveling waves
• General solution as a superposition of traveling waves
• Wave pulses, reflection at a fixed boundary
• DEMOs: wave pulses on a spinning chain and on Bell Labs wave machine, addition of sine waves to give standing waves, stationary initial pulse on the Bell Labs wave machine and on a long spring

L11 - Wed, March 11

• Derivation of the wave equation for longitudinal sound waves in pipes
• The speed of sound
• Normal modes for pipe open at both ends
• Normal modes for pipe open at one end and closed at the other
• Physics of wind instruments
• DEMOs: trombone, trumpet, flute, clarinet, opening and closing the end of a flute, helium in a flute, helium in prof's lungs, standing sound waves in plexiglas tube driven by speaker, longitudinal oscillations of bars, normal modes of Bell-Labs wave machine with two free ends, one free one fixed, and with two fixed ends

L12 - Mon, March 16

L13 - Wed, March 18

L14 - Mon, March 30

• Electrical and mechanical transmission lines
• Derivation of the wave equation for voltage and current
• Capacitance and inductance per unit length, speed of propagation
• Coaxial cable: calculation of the inductance and capacitance per unit length
• Characteristic impedance of a transmission line
• Power transmitted by a traveling wave
• DEMOs: pulse propagation and reflection on a coaxial cable, microwave propagation in parallel plate line, coaxial cable terminated on its characteristic impedance

L15 - Wed, April 1

• Reflection coefficient for a general complex load impedance
• Reflection/transmission at boundary, energy conservation
• Characteristic mechanical impedance of a vibrating string
• Standing waves on a transmission line, input impedance
• Resistance and attenuation
• DEMOs: Bell Labs wave machine correctly terminated on a damper, reflection between two sections, standing waves on Lecher lines, impedance matching by tapered section, megaphone

L16 - Mon, April 6

• Wave propagation in 3-D, wave fronts, plane waves, wave vector
• EM waves in a transmission line
• Derivation of the wave equation from Maxwell's equations
• EM plane waves in vacuum
• DEMOs: radio wave propagation, AM radio, microwaves

L17 - Wed, April 8

• E and B fields of an EM plane wave
• Poynting vector, intensity, energy density in an EM wave
• Energy conservation, luminosity vs intensity, isotropic sources
• Examples of sources and orders of magnitude of intensities
• Linear polarization, polarizers
• Elliptical and circular polarization
• DEMOs: circular polarization on a vibrating string, polarization of microwaves, light going through two crossed polarizers

L18 - Mon, April 13

• 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)

L19 - Wed, April 15

L20 - Wed, April 22

• Classical model of atomic vibrations, radiative damping
• Scattering by atoms, scattering cross section
• Rayleigh, Thomson, and resonant scattering
• Examples: solar corona, lunar eclipses, absorption spectra, blue sky and red sunsets
• DEMOs: scattering of light by water - polarization of scattered light, sunset on Venice Beach, scattering of light by cigar smoke

L21 - Mon, April 27

• Interference from a linear array of N sources
• Intensity vs phase, radiation patterns for 2 and N sources
• Phased arrays
• DEMOs: interference from 2 speakers, 2 microwave horns, 2 slits in ripple tank
• PLOTs: I vs delta, radiation patterns from 2 and N sources

L22 - Wed, April 29

L23 - Mon, May 4

• Multiplication of beam patterns, array of dipoles
• Far field (Fraunhofer limit) vs near field (Fresnel limit)
• The continuous limit for N sources in a linear array
• Diffraction through a rectangular aperture
• Diffraction-limited beams
• Diffraction gratings
• DEMOs: diffraction of laser light through narrow slit and circular pinhole, diffraction through narrow slit in ripple tank, transmission grating with laser, looking at various sources through diffraction gratings

L24 - Wed, May 6

• Huygens Principle applied to diffraction
• Index of refraction, wavelength in a dielectric
• Laws of reflection and refraction, total internal reflection
• Reflection and refraction as interference processes
• Polarization by reflection, the Brewster angle
• DEMOs: reflection and refraction of laser light at water-air interface, total internal reflection, polarization by reflection, Brewster angle for air-glass interface

L25 - Mon, May 11

L26 - Wed, May 13