### Cable Tension and Shape on a Suspension Bridge

## by Ahmed Al-Khalil

Submitted : Fall 2012

The objective is to find the point ‘A’ where the cable hangs the lowest, the relatives distances ‘x’ and ‘y’ from the origin, and to plot a graph of the cable tension ‘T’ vs. ‘x’ and the shape of the cable ‘y’ vs. ‘x’. There are five unknowns that we need to find, (x_{1}, x_{2}, y_{1}, y_{2}, T_{0}). Where x_{1} = distance from origin to left end, x_{2} = distance from origin to right end, y_{1} = height of the cable at left end, y_{2} = height of the cable at right end, T_{0} = lowest tension on cable, at the point (0,0). I was able to find the T_{0}, which the problem asks for, using the arc length formula. I have five equations and five unknowns. With T_{0} I was able to find the other unknowns mostly by using substitution between the other four equations.

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