The system is released from rest with no slack in the cable and with the spring stretched $220$ mm$.$ Determine the distance s traveled by the $20$ kg cart before it comes to rest $($a$)$ if m approaches zero and $($b$)$ if m $=5\mathrm{.}4$ kg$.$ Assume no mechanical interference. $($DYNAMICS problem: Kinetics of Particles, please using corresponding formulas and techniques$).$