MATLAB #3 - David Thibodeaux MATH 111-H03 MATLAB...

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Picture 1 David Thibodeaux MATH 111-H03 MATLAB Assignment #3 11/27/10 Introduction: In this assignment, we will observe the behavior of a suspended chain, and the properties of its curvature. Using Newton’s method, we will also determine the constant a, which is used to define the catenary curve that the chain adopts. Part 1: Analytical Calculation Before moving on, let’s look at a visual representation of the suspended chain: We are given the equation for the catenary curve: f(x) = a cosh (x/a) + C. We know from the given figure that the height at which the chain is highest is the point [p, f(p)] or [–p, f(-p)], and the height at which the chain is lowest is [0,f(0)]. Therefore, the difference in height (s) is given by s = f(p) – f(0) or s = (acosh(p/a) + C) – (acosh(0) + C) since cosh(0) is 1, we get: s = acosh(p/a) + C – a – C or s = acosh(p/a) – a Part 2:
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Picture 3 Picture 1 Picture 4 Picture 11 Picture 12 Picture 3 Picture 8 Picture 10 Picture 13 We start with the following equations: and
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