1. The problem statement, all variables and given/known data Three equal weights are suspended from the midpoint of three spans of a near-horizontal negligible-mass wire supported at frictionless pulleys, and are counterbalanced by an adjustable spring set to exert an initial nominal force of 3W, this spring force being increased as the weights are 'pulled up'. The wire is fixed at point x. See attached gif. I'm trying to determine the tensions t1, t2, t3, t4, t5 and t6. 2. Relevant equations Taking the left-hand span, as a1 approaches zero, the vertical components (t1cosa1, t2cosa1) of t1 and t2 will approach t1 and t2 respectively, with t1 being equal to t2, since the attachment point of the weight to the wire does not move. Similarly, in the other spans, t3 = t4, and t5 = t6. For the vertical components (t1sina1, t2sina1) of t1 and t2, the sum of these will equal W: t1sina1 + t2sina1 = W Since t1 = t2, this vertical can be expressed as: t2 = W/2sina1 (Similarly, in the other spans, t4 = W/2sina2, and t6 = W/2sina3.) 3. The attempt at a solution As the angles approach zero, so does sina, and the vertical expressions indicate the tension needs to be increasingly large. If the tensions are considered bidirectional, then I think the sum t1 + t2 + t3 + t4 + t5 + t6 will be equal to the force needed to be exerted by the spring, but I don't have any relationship between the angles a1, a2 and a3, and therefore I can't prove that t1 = t2 = t3 = t4 = t5 = t6, which intuitively would seem to be the case in the near-zero angle case.