$.$ For the simple harmonic oscillation of Example $4($where k $=19\mathrm{.}6$ N$/$m$,$ A $=0\mathrm{.}100$ m$,$ x $=-(0\mathrm{.}100$ m$)$ cos $8\mathrm{.}08$t$,$ and v $=(0\mathrm{.}808$ m$/$s$)$ sin $8\mathrm{.}08$t$),$ determine $($a$)$ the total energy, $($b$)$ the kinetic and potential energies as a function of time, $($c$)$ the velocity when the mass is $0\mathrm{.}050$ m from equilibrium, $($d$)$ the kinetic and potential energies at half amplitude $($x $=$ A$/2)$