Answered: A chain with length l is held stretched…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A chain with length l is held stretched out on a frictionless horizontal table, with a length y0 hanging down through a hole in the table. The chain is released. As a function of time, find the length that hangs down through the hole (don’t bother with t after the chain loses contact with the table). Also, find the speed of the chain right when it loses contact with the table. (Assume that the chain moves straight down through the hole ... i.e. ignore that the chain would overshoot due to momentum. Also assume that the chain has a constant mass per unit length) Finally, you will get to the point that you have an equation of the form: ¨y = Cy (where C is a constant). This has a solution of the form: y = Ae √ Ct + Be− √ Ct where A and B are constants of integration that you can solve for with your initial conditions. (And you can confirm this is really a solution by taking the second derivative!)

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