phys 224 - introductory physics iii - spring 2008 prof. j. vanderlei martins umbc department of...
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PHYS 224 - Introductory Physics III - Spring 2008
Prof. J. Vanderlei MartinsUMBC Department of Physics
Oscillations and Wavesfrom: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
Interacting Pulsesfrom: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
Interacting Pulses – same direction from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
Adding Traveling Waves from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
Adding Traveling Waves from: http://www.maths.gla.ac.uk/~fhg/waves/waves1.html
Superposition of Simple Harmonic MotionBeat: Results from adding two harmonic oscillations with similar frequencies.
Beat
http://www.kettering.edu/~drussell/Demos/superposition/superposition.html
Lissajous Figures:
Number of tangents in each axes provides information on the period ratio
Figure Credit:http://en.wikipedia.org/wiki/Lissajous_curve
o = 60dgo = 15dg
Simple Pendulum Small angle approximation: sin() ~
How small is small?
http://www.kettering.edu/~drussell/Demos/Pendulum/Pendula.html
Solutions:
Exact:
F = -mg•sin(
Approximation:
F = -mg•
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.
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()
Waves are the key to sound, color, and much more:
• Rainbow• Sunglint• Tsnunamis• Earthquakes• Cel Phone signals• Microwave ovens• Musical Instruments• …
http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/raibowcon.html#c1
Rainbow Physics
Cloud Rainbow observed from space:F-M. Breon, P. Goloub, 1998.
The Sunglint
• What is its connection with oscillations and waves?
Picture by Yoram Kaufman
Sunglint:Windy and Polluted Day
Sunglint:“Calm and Clean” Day
Picture by Yoram Kaufman
http://deathstar.rutgers.edu/projects/viewnj/pages/STS066-150-074.htm