Computational_Problems.md

Physics

Cantilever Problem

There are two poles with pulleyes at the tops of these poles at positions $x_1$ and $x_2$, heights $y_1$ and $y_2$, and an infinitely long chain of mass density $\lambda$ is strung across the pulleyes.

The cantilever problem is to find the equation representing the position of each point on the chain between the two poles. The solution is: $y(x) = a\cosh{\left(\frac{x-b}{a}\right)}$

Given that $x_1=0$ and $x_2=1$, numerically determine possible values of $a$ and $b$ in the following scenarios:

1. If $y_1=y_2=1$
2. If $y_1=1$ and $y_2=0.8$
3. If $y_1=1$ and $y_2=0.6$

Your Python solution should follow the following format:

# "Business code"

if __name__ == "__main__":
    # calls whatever functions or classes defined above to obtain the values of a and b in each scenario

Whether you want to define a function or method that returns the values of a and/or b and then print the return value of that function in your __name__ == "__main__" block or have your functions or methods print the values is up to you. There are no restrictions on what libraries you can use.