1. Statement of the problem statement, including all variables I am working the following example in my book: A light string of length b is attached at point A, passes a pulley B located a distance 2d away, and finally attached to a mass m1. Another pulley with mass m2 attached passes over the string, pulling it down between A and B. Calculate the distance x1 when the system is in equilibrium. The pulleys are massless. The book works the problem in terms of the energy paradigm, however I am working the problem in terms of the force paradigm (I need the practice). I have had a bit of trouble with seeing what forces are acting where, but think I have finally nailed it and am looking for a second opinion to see if I am right for the right physical reasons. Please excuse my use of the attached pictures As I am currently without my laptop and therefore am without an adequate and convenient means of displaying LateX. 2. Relevant equations See attached equation file. 3. The attempt at a solution The basic idea is that I use the equality derived from the Sine equation listed to give me an quality that I may use to solve for x1 in terms of the masses, b, and d. I get the original Sine equality from the fact that the Tension becomes split among the two triangles when the pulley with the second mass is added in the manner indicated in the attached diagram (System2). Thus the upward felt force on the second mass from one of these split Tension vectors is equal to half the weight of the second mass due to the fact that the Tension is split evenly and that neither mass experiences any acceleration. Does this seem valid? When I do this I get that the equilibrium position of x1 is b minus the term d times the ratio of 4m1 to the square root of 4(m1)2-(m2)2.