1. PHYS 224 - Introductory Physics III - Spring 2008 Prof. J. Vanderlei Martins UMBC Department of Physics

2. Oscillations and Waves from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html

3. Interacting Pulses from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html

4. Interacting Pulses – same direction from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html

5. Adding Traveling Waves from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html

7. Superposition of Simple Harmonic Motion Beat: Results from adding two harmonic oscillations with similar frequencies. Beat http://www.kettering.edu/~drussell/Demos/superposition/superposition.html

8. Lissajous Figures: Number of tangents in each axes provides information on the period ratio Figure Credit: http://en.wikipedia.org/wiki/Lissajous_curve

9.  o = 60dg  o = 15dg Simple Pendulum Small angle approximation: sin(  ) ~  How small is small? http://www.kettering.edu/~drussell/Demos/Pendulum/Pendula.html

10. Solutions: Exact: F  = -mg sin(  Approximation: F  = -mg 

11. Comparing Solutions: Check the link below for simulations: http://www.kettering.edu/~drussell/Demos/Pendulum/Pendula.html Up to ~15 degrees initial displacement, the small angle approximation holds well and even after several oscillations the approximate solution compares well with the “exact” solution. For larger angles (e.g. the 60 dgs shown in the simulation, the approximate solution diverges quickly from the “exact” result.

13. Waves are the key to sound, color, and much more: Rainbow Sunglint Tsnunamis Earthquakes Cel Phone signals Microwave ovens Musical Instruments …

14. http://hyperphysics.phy- astr.gsu.edu/hbase/atmos/raibowcon.html#c1 Rainbow Physics

15. Cloud Rainbow observed from space: F-M. Breon, P. Goloub, 1998.

16. The Sunglint What is its connection with oscillations and waves?

17. Picture by Yoram Kaufman Sunglint: Windy and Polluted Day

18. Sunglint: “Calm and Clean” Day Picture by Yoram Kaufman

19. http://deathstar.rutgers.edu/projects/viewnj/pages/STS066-150-074.htm