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# Physics 152: Oscillations and Waves

*Michael Fowler UVa*

*PDF of notes on Oscillations and Waves*

## Lectures and Applets on Oscillations and Waves

1. From Complex Numbers to the Simple Harmonic Oscillator PDF Applet

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

**2. Heavily Damped Simple Harmonic Oscillator** Applet

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

3. Lightly and Critically Damped Oscillations Applet

*From ringing a bell to checking your shocks.*

4. Driven Damped Oscillators Applet

*From picking up a cell signal to wrecking a bridge.*

PDF of the above three lectures

**6. Introducing
Waves: Strings and Springs PDF
**

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

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

**8. Boundary Conditions PDF** Applet

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

*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** Applet

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

**11. The Doppler Effect PDF** Applet

## 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 Possibly this approach is being superseded by, say, using Python.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.*

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

### 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