Problem 19

# Problem 19 - computation method Given a value of d and h we...

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ECOR1606 Problem Solving and Computers Page 1 of 1 Department of Systems and Computer Engineering, Carleton University Summer 2003 Assignment – Catenary A catenary is the curve formed by a hanging cable (Figure 1). Assume that the lowest point of the cable is located at (0,0), the catenary can be described by the equation C C x cosh C y - = where cosh is the hyperbolic cosine. Figure 1 There are two towers spaced d meters apart that have a height of h meters. We want to find the catenary equation that describes a cable connecting the tops of the towers which droops 2 meters. ( 29 2 h C C x cosh C y - + - = To find the equation of the catenary, we need to solve for C. Trying to do this analytically (i.e. re-arranging this equation) is difficult so we will attempt to do this using a
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Unformatted text preview: computation method. Given a value of d and h, we can rearrange the equation so that it is a root finding problem (i.e. find an equation f(C) = 0). Write a program that accepts values for d and h, and that determines the equation of the catenary. Use the bisection method to find the root and ensure your approximation of C is accurate to 5 decimals places. You can use the starting interval of [0.00001,10000] to find the value of C. Your program should check if this is a valid starting interval (i.e. f(0.00001) and f(10000) have opposite signs). Your program should also check the inputs for the d and h to ensure that d is positive and nonzero, and that h is greater than 2. Users should be re-prompted to enter the information if the input was not valid....
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