ME218 Lecture 13 Presentation

# ME218 Lecture 13 Presentation - Where are we 1 Higher Order...

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Where are we? 1

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Higher Order ODE-s (to be repeated) 2 0 ) , ( ... 1 2 2 2 1 1 1 = + + + + + - - - y x f dx dy a dx y d a dx y d a dx y d a n n n n n n 1 2 3 2 2 1 2 2 1 1 z y z dx dy z dx y d z dx y d z dx y d n n n n n n = = = = = - - - - - 2 1 3 2 1 2 1 ? z dx dz z dx dz z dx dz z dx dz dx dz n n n n n = = = = = - - - 0 ) , ( ... 1 2 1 3 2 1 = + + + + + - z x f z a z a z a dx dz a n n n n
Overview of Differential Equations 3

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Where are we? 4
Sagging of a Cable: Boundary Value Problem Dr. Dragan Djurdjanovic ME 218 Fall 2011

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The Problem Power transmission lines, generally, have cables that have significant weight of their own. This causes the cable to sag. Some amount of sag is also necessary to account for the thermal expansion and contraction during seasonal changes. The sag can be controlled by adjusting the tension in the cable by applying a force (T) at the two ends. T T w(x) x Load distribution
The sag ( w ) of a flexible cable is governed by the equation: Where

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ME218 Lecture 13 Presentation - Where are we 1 Higher Order...

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