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

PHYS 224 - Introductory Physics III - Spring 2008 Prof. J. Vanderlei Martins UMBC Department of Physics. Oscillations and Waves from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html. Interacting Pulses from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html.

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

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

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

  3. Interacting Pulsesfrom: 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

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

  7. Superposition of Simple Harmonic MotionBeat: 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. Simple Pendulum Small angle approximation: sin(q) ~ qHow small is small? qo = 15dg qo = 60dg http://www.kettering.edu/~drussell/Demos/Pendulum/Pendula.html

  10. Solutions: Exact: Fq = -mg•sin(q) Approximation: Fq = -mg•q

  11. Comparing Solutions: 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. Check the link below for simulations: http://www.kettering.edu/~drussell/Demos/Pendulum/Pendula.html

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

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

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

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

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

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

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

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