1) Find a general equation for x(t), the length of rope through the hole.
2) Evaluate the constants A and B so that the initial conditions are satisfied
Please see the attached file.
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The solution shows how to translate the language of the problem into a solvable differential equation. The solution then continues to solve the equation of motion. The full solution file contains 4 pages in an attached Word and PDF copy including diagrams and all derivations.