$3\mathrm{.}9.$ A cam in a large machine can be modeled as applying a $15,000N-$force over an interval of $0\mathrm{.}01$ s $.$ This can strike a valve that is modeled as having physical parameters: $m=10kg,c=20N\frac{s}{m},$ and stiffness $k=8000\frac{N}{m}.$ The cam strikes the valve once every $1$ s $.$ Calculate the vibration response, $x(t),$ of the valve once it has been impacted by the cam. The valve is considered to be closed if the distance between its rest position and its actual position is less than $0\mathrm{.}0001$ m $.$ Is the valve closed the very next time it is hit by the cam?