The kinetic sculpture requires that each of the three pinned beams be in perfect balance...

The kinetic sculpture requires that each of the three pinned beams be in perfect balance at all times during its slow motion. If each member has a uniform weight of 2 lb/ft and length of 3 ft, determine the necessary counterweights W₁, W₂, and W₃ which must be added to the ends of each member to keep the system in balance for any position. Neglect the size of the counterweights.