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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.

Spreadsheet for Damped Oscillator

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

Spreadsheet for Damped Driven Oscillator

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

Pendulum Spreadsheet

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

Introducing Waves: Strings and Springs         PDF  

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.

Boundary Conditions   PDF

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.

The Doppler Effect    PDF 


Waves: Flashlets,  Links

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.

Flashlet of Air Motion as a Sound Wave Travels Down a Tube  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


Wave Spreadsheets

Animated Spreadsheet for Adding Harmonic Traveling Waves to Get Standing Waves

Animated Spreadsheet for Two Traveling Waves

Building a Triangular Wave: Fourier Series

Spreadsheet for Beats, Group Velocity and Phase Velocity


For Students, Problem Sets and Study Sheets:

Oscillator Homework Problems  PDF


Waves Homework Problems  PDF


Oscillations: the Essentials   PDF


Waves: the Essentials   PDF



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