Hanging cable

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A cable is suspended between two towers like a power line between two towers. Assume that the towers are on a level parcel of ground but the heights of the towers maybe different. Using the following notation

- height of cable center

- distance between two towers

- height of cable at tower 1

- height of cable at tower 2.

- horizontal component of tension.

units of weight per unit length of cable.

and the forces acting on the cable, it can be shown that the cable height is the solution of the differential equation

with the end conditions and .