I was working on a pulley system as shown here: The mass on the right and left side is equivalent, and I am solving for when the system is in static equilibrium. Theta is the angle between the rope on either side of one of the pulleys. H and y are both measured from the original position of mass M, not its current location (it was simply meant as a reference point). The mass of the rope and friction are ignored. I wanted to find how the distance y changes as the mass x changes. I first found the acceleration of the object, which is of course 0: I then solved for theta, giving me: I then was able to find cosΘ: And I was then able to find the final equation by setting the first equation equal to 0: Here is a link to the graph: https://www.desmos.com/calculator/wpttkfsvmb I imagine that this system may be used as a balance, in which the sag of the rope tells you the mass of x as based on the equation. Would that be possible? Thanks in advance. (As a side note, I feel dumb showing my work in the form of images, but I can't figure out how to use BB code editor—I might just be missing something obvious).