Catenary cable is one which is hung between two points not in the same vertical line. It is subject to no loads other than its own weight. Thus, its weight acts as a uniform load per unit length akong the cable w (N/m). A free-body diagram of a section AB is depicted in the figure, where T, and T, are the tension forces at the end. Based on horizontal and vertical force balances, the following differential equation model of the cable can be derived: d'y dr Calculus can be employed to solve this equation for the height of the cable y as a function of distance x: y = cosh )+ ya -4 T. Homework 2 a. Use a numerical method to caleulate a value for the parameter T, given values for the parameters w- 10 and yo= 5, such that the cable has a height of y- 15 at x- 50. b. Develop a plot of x versus y for x--50 to 100.