$.(12$ points$)$ A mass weighing $16$ lb stretches a spring $8$ in$.$ There is no damping. At the initial time t $=0$ the mass is pushed upward, contracting the spring by a length of $6$ in$,$ and set in motion with a downward velocity of $2$ ft$/$s$.$ Find the values of the mass and spring constant and set up the initial value problem but do not solve. You may assume that gravitational acceleration is $32$ ft$/$s$2.$