A metal block, placed on a rough surface, is attached to a spring and is given an initial displacement of \(10 \mathrm{~cm}\) from its equilibrium position. It is found that the natural time period of motion is \(1.0 \mathrm{~s}\) and that the amplitude reduces by \(0.5 \mathrm{~cm}\) in each cycle. Find

(a) the kinetic coefficient of friction between the metal block and the surface and

(b) the number of cycles of motion executed by the block before it stops.