Blocks A and B are connected by a cord that passes over pulleys and through a collar C$.$ The system is released from rest when x $=1\mathrm{.}7$ m$.$ As block A rises, it strikes collar C with perfectly plastic impact $($e $=0).$ After impact, the two blocks and the collar keep moving until they come to a stop and reverse their motion. As A and C move down, C hits the ledge and blocks A and B keep moving until they come to another stop. Determine $($a$)$ the velocity of the blocks and collar immediately after A hits C$,($b$)$ the distance the blocks and collar move after the impact before coming to a stop, $($c$)$ the value of x at the end of one complete cycle.