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

Previewing pages 1, 2, 17, 18, 19, 35, 36 of 36 page document
View Full Document

# The Pit and the Pendulum

Previewing pages 1, 2, 17, 18, 19, 35, 36 of actual document.

View Full Document
View Full Document

## The Pit and the Pendulum

58 views

Other

Pages:
36
School:
College of the Redwoods
Course:
Math 55 - Differential Equations
##### Differential Equations Documents
• 25 pages

• 28 pages

• 30 pages

• 21 pages

• 21 pages

• 11 pages

• 35 pages

• 32 pages

• 32 pages

• 15 pages

• 16 pages

• 16 pages

• 26 pages

• 20 pages

• 24 pages

• 29 pages

• 20 pages

• 9 pages

• 47 pages

• 27 pages

• 15 pages

• 16 pages

• 16 pages

• 21 pages

• 22 pages

• 21 pages

• 26 pages

• 18 pages

• 20 pages

• 16 pages

• 21 pages

• 22 pages

• 28 pages

• 27 pages

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

View Full Document

Unlocking...