# Physics 152:  Oscillations and Waves

Michael Fowler UVa

### Oscillations: Lecture Notes

From Complex Numbers to the Simple Harmonic Oscillator  PDF

Damped and/or Driven Oscillators   PDF

The Pendulum   PDF

### Oscillations: Spreadsheet Demos and a Spectacular Demo

SHM as the Shadow of Circular Motion

A very simple spreadsheet animating the process. Press and hold the end of thescrollbar.

This spreadsheet plots the motion of a damped oscillator: you can specify the initial conditions and degree of damping, and find critical damping.

An external driving force is added to the previous spreadsheet: see how damping and resonance compete.

Find out how the period of a real pendulum varies with the amplitude.

Crazy Way to Demonstrate Simple Harmonic Motion

From Vladimir Vasc, in the Czech Republic.

### Waves: Lecture Notes

Kinds of waves in one dimension: transverse, longitudinal, traveling, standing.

Analyzing Waves     PDF

How applying F = ma to a little piece of string leads to an equation that describes many different waves.

What happens to a wave when it reaches the end of the string?

Sound Waves     PDF

Deriving the Wave Equation for sound waves in a pipe.  Energy density and power in a sound wave in a pipe.

Waves in Two and Three Dimensions   PDF

Extending the Wave Equation to higher dimensions.  Huygens’ picture of wave propagation.  Young’s two-slit measurement of the wavelength of light.

Flashlet of Tension Forces on a Bit of a Waving String

JavaScript applet of waving string

Finding these forces and applying Newton’s Law to a small piece of  string is the way to the Wave EquationFlashlet by Patrick LeDuc.

Water Waves from Two Point Sources    Java Applet by Santosh Pisharody

Interference from Two Sources: Young’s Two Slit Experiment

Flashlet for The Doppler Effect

Great Website for Sound and Musical Instruments

Some Applets

Animated Spreadsheet for Two Traveling Waves

Building a Triangular Wave: Fourier Series

Spreadsheet for Beats, Group Velocity and Phase Velocity