Challenges - Calculus - 200827

This problem is called ring on a string. The output of this problem can be applied in many aspects of life, for example, when constructing a bridge. Here is the question:

You are given a string of fixed length. Now thread it through the ring of fixed weight. The two ends of the string are in a fixed location too, let’s say, coordinate (0,0) and coordinate (a,b). And the ring is now in a coordinate of (x,y). Find x,y (or any other conditions) so that the ring reaches an equilibrium point.

The problem can be summarized in the graph below:

You have one day to work out the answer. I will published the official one tomorrow ^^.

Good luck!

To reveal the answer, click below