CR MATH 55 - The Pit and the Pendulum (36 pages)

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The Pit and the Pendulum



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The Pit and the Pendulum

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Pages:
36
School:
College of the Redwoods
Course:
Math 55 - Differential Equations

Unformatted text preview:

The Pit and the Pendulum Introduction Modeling Poe s Modeling Poe s Aaron Kavanaugh and Travis Moe A System of Equations A Change of Variables May 12 2005 Finding Initial Computing and Abstract Edgar Allen Poe wrote some of the most original and terrifying horror stories of the 19th century Poe s protagonists often met with grizzly deaths His classic The Pit and the Pendulum is no exception to this In Poe s story a man is strapped to a table and forced to watch as a ever lengthening pendulum tipped with a scythe swings closer and closer to his chest In this paper we investigate not the psychological but the physical aspects of a lengthening pendulum We describe the lengthening pendulum in terms of Newtonian and Lagrangian mechanics and derive a differential equation for the pendulum s motion in terms of its angle We then examine numerical methods of solving this differential equation and transform our differential equation into a Bessel equation to discover an analytical solution Finally we examine the motion of such a pendulum in reference to Poe s story While our paper may not be as terrifying as a Poe tale unless you regard intense applications of the chain rule terrifying it is sure to be more informative Conclusion Acknowledgements Appendix Home Page Title Page JJ II J I Page 1 of 36 Go Back Full Screen Close Quit 1 Introduction Looking upward I surveyed the ceiling of my prison It was some thirty or forty feet overhead and constructed much as the side walls In one of its panels a very singular figure riveted my whole attention It was the painted figure of Time as he is commonly represented save that in lieu of a scythe he held what at a casual glance I supposed to be the pictured image of a huge pendulum such as we see on antique clocks There was something however in the appearance of this machine which caused me to regard it more attentively While I gazed directly upward at it for its position was immediately over my own I fancied that I saw it in motion In



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