Posted: February 27th, 2023

Discussion Reply: Cable under Self-Weight

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For the problem of a cable under its own weight we have a differential
equation of:

Using this differential equation and assuming the cable is of
uniform weight density, we can determine the function of the
curve that will occur when hung by each end at uniform
height. By taking a small segment of the curve inside an
interval you can use the tension and tangent angels at each
end along with the weight of the cable you can find the sag
of the cable under it’s own weight.

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