A particle of mass m slides along a curved-flat-curved track. The curved portions of the track are smooth. If the particle is released at the top of one of he curved portions, the particle comes to rest at flat portion of length l and of \(\mu = \mu_{kinetic}\) after covering a distance of : 

\(\frac{H}{\mu_{kinetic}}\)

\(\text{Here, according to ques : }\)

\(\text{PE = Work done}\)

\(mgH = \mu_{kinetic} m g S\)

\(\Rightarrow S = \frac{H}{\mu_{kinetic}}\)

The particle covers the length l or not or covers it repeatedly is determined by the above relation.