[CSC 415] The Period of the Pendulum

[Andrew J. Pounds]

The period of a pendulum is the time it takes a pendulum to move from 
its starting point back to that point.  In other words the time for a 
swing forward plus the time for a swing back.  If we make the assumption 
that $\theta$ is small so that $\theta \approx \sin(\theta)$ then the 
period of the pendulum is given by the equation seen in most general 
physics books.

$T = 2 \pi \sqrt{\frac{l}{g}}$

The problem we have is that our pendulum aren't idealized and cannot use 
the assumption mentioned above.   For that reason I have included a 
Mathematica notebook that I built this evening that will calculate the 
period of the pendulum based on $\theta$ not being close to 0.   I used 
the "standard second" pendulum length of 0.994 m and standard gravity.  
With $\theta$ being small this gives something very close to the correct 
answer of 2 seconds for the pendulum.  We will talk more about this in 
class on Thursday, but feel free to play with the Mathematica notebook 
and see what happens if you change the initial $\theta$ to something 
like $\pi$/2.


-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627
http://faculty.mercer.edu/pounds_aj

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