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Unformatted text preview: Pictu re 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: Pictu re 3 Pictu re 1 Pictu re 4 Pictu re 1 Pictu re 1 2 Pictu re 3 Pictu re 8 Pictu re 1 0 Pictu re 1 3 We start with the following equations:...
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This note was uploaded on 03/22/2011 for the course BME 111 taught by Professor Gokce during the Spring '11 term at NJIT.
- Spring '11