Physics 152: Oscillations and Waves

Michael Fowler UVa


PDF of notes on Oscillations and Waves


Lectures on Oscillations and Waves

1.   From Complex Numbers to the Simple Harmonic Oscillator  PDF

Complex numbers are the key to analyzing oscillations and waves easily.

2.  Heavily Damped Simple Harmonic Oscillator

Surprisingly, the heavily damped case is the easiest mathematically, and has some interesting physics.

3.  Lightly and Critically Damped Oscillations

From ringing a bell to checking Your shocks.

4.  Driven Damped Oscillators

From picking up a cell signal to wrecking a bridge.

PDF of the above three lectures

5,  The Pendulum   PDF

6.  Introducing Waves: Strings and Springs   PDF  

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

7.  Analyzing Waves   PDF

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

8.  Boundary Conditions  PDF

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

9.  Sound Waves   PDF

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

10.  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.

11.  The Doppler Effect  PDF


Other Course Materials

Spreadsheets

I found in teaching this course in the past that constructing Excel spreadsheets and exploring with them proved useful in building intuition. Possibly this approach is being superseded by, say, using Python. Anyway, here are the spreadsheets.

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.

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