Chapter 28, Problem 25P

A cable is hanging from two supports at A and B (Fig. P28.25). The cable is loaded with a distributed load whose magnitude varies with x as

$\omega ={\omega }_0\left[1+\text{sin }\left(\frac{\pi x}{2l_A}\right)\right]$

where $w_0=1000\text{ Ib/ft}$. The slope of the cable $\left(dy\text{/}dx\right)=0\text{ at }x=0$, which is the lowest point for the cable. It is also the point where the tension in the cable is a minimum of $T_0$, The differential equation that governs the cable is

$\frac{d^{2}y}{d{x}^2}=\frac{{\omega }_o}{T_o}\left[1+\text{sin }\left(\frac{\pi x}{2l_A}\right)\right]$

Solve this equation using a numerical method and plot the shape of the cable $\left(y\text{ versus }x\right)$. For the numerical solution, the value of $T_o$ is unknown, so the solution must use an iterative technique, similar to the shooting method, to converge on a correct value of $h_A$ for various values of $T_o$.