Problem pts$)$

The equation for a reflected standing wave in a harbor is given by:

$h=h_0[sin(\frac{2x}{})cos(\frac{2tv}{})+e^{-x}]$

with $=16,t=12,v=48,h=0\mathrm{.}4h_0.$ Use Python to implement the secant method to find the

value of $x$ that corresponds to the maximum $h.$ Select an initial guess pair $(x_0,x_1)$ from one of

the following: $(0,2\mathrm{.}5),(3,5),$ or $(10,13).$ Use the stopping criteria

where the significant figure $d=7.$ Display each iteration in the format: $($ # Iteration, $x_r,g(x_n),{}_a).$

Provide the Python code along with the iteration results.

Hint: Choose your initial guesses based on graphical insight, and the total number of iterations

should be fewer than six to meet the specified error tolerance.

Problem $2(40$ pts$)$:

A catenary cable is one that hangs between two points that are not vertically aligned and is

subjected only to its own weight. The weight of the cable $(\frac{N}{m})$ acts as a uniform load per

unit length along its length. A free$-$body diagram of a section AB is depicted below:

$($a$)$

$($b$)$

where $T_A$ and $T_B$ are the tension forces at the end. By using calculus, the equation for the height

$y$ of the cable as a function of $x$ can be derived as:

$y=\frac{T_A}{w}cosh(\frac{w}{T_A}x)+y_0-\frac{T_A}{w}$

Given the parameter values $w=10,y_0=5,$ and $y=15$ at $x=50,$ calculate $T_A.$