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![Page 1: PHYS 224 - Introductory Physics III - Spring 2008 Prof. J. Vanderlei Martins UMBC Department of Physics.](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649edf5503460f94befcca/html5/thumbnails/1.jpg)
PHYS 224 - Introductory Physics III - Spring 2008
Prof. J. Vanderlei MartinsUMBC Department of Physics
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Oscillations and Wavesfrom: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
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Interacting Pulsesfrom: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
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Interacting Pulses – same direction from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
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Adding Traveling Waves from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
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Adding Traveling Waves from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
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Superposition of Simple Harmonic MotionBeat: Results from adding two harmonic oscillations with similar frequencies.
Beat
http://www.kettering.edu/~drussell/Demos/superposition/superposition.html
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Lissajous Figures:
Number of tangents in each axes provides information on the period ratio
Figure Credit:http://en.wikipedia.org/wiki/Lissajous_curve
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o = 60dgo = 15dg
Simple Pendulum Small angle approximation: sin() ~
How small is small?
http://www.kettering.edu/~drussell/Demos/Pendulum/Pendula.html
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Solutions:
Exact:
F = -mg•sin(
Approximation:
F = -mg•
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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.
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6.2
6.25
6.3
6.35
6.4
6.45
6.5
0 10 20 30 40 50
angle (dg)
Pe
rio
d (
s)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Re
lati
ve
Dif
fere
nc
e (
%)
Approximation Exact % Diff.
Comparing Solutions:F=-mg
xF = -mg sin()
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Waves are the key to sound, color, and much more:
• Rainbow• Sunglint• Tsnunamis• Earthquakes• Cel Phone signals• Microwave ovens• Musical Instruments• …
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http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/raibowcon.html#c1
Rainbow Physics
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Cloud Rainbow observed from space:F-M. Breon, P. Goloub, 1998.
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The Sunglint
• What is its connection with oscillations and waves?
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Picture by Yoram Kaufman
Sunglint:Windy and Polluted Day
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Sunglint:“Calm and Clean” Day
Picture by Yoram Kaufman
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http://deathstar.rutgers.edu/projects/viewnj/pages/STS066-150-074.htm