solid cylinder attached to a horizontal spring $($k$=9\mathrm{.}30$N$/$m$)$ rolls without slipping along a horizontal surface. if the system is released from rest when the spring is stretched by $0\mathrm{.}170$m$,$ find $($a$)$ the translational kinetic energy and $($b$)$ rotational kinetic energy of the cylinder as it passes through the equilibrium position. $($c$)$ if the cylinder has mass M$=4\mathrm{.}20$kg$,$ find the period of the simple harmonic motion that the cylinder's center of mass executes.