Solved: Using principles from physics it can be shown that when a cable is hung between

Chapter 3, Problem 3.11.52

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Using principles from physics it can be shown that when a cable is hung between two poles, it takes the shape of a curve y ! f !x" that satisfies the differential equation d2 ydx 2 ! /tT '1 $ %dydx &2 where is the linear density of the cable, is the accelerationdue to gravity, and is the tension in the cable at its lowestpoint, and the coordinate system is chosen appropriately.Verify that the function y ! f!x" ! T/t cosh%/txT &is a solution of this differential equation.

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