$2\mathrm{.}59.$ A very common example of base motion is the single$-$degree$-$of$-$freedom model of an automobile driving over a rough road. The road is modeled as providing a base motion displacement of $y(t)=(0\mathrm{.}01)sin(5\mathrm{.}818t)m.$ The suspension provides an equivalent stiffness of $k=3\mathrm{.}273{10}^4\frac{N}{m},$ a damping coefficient of $c=231kg,$ and a mass of $1007$ kg $.$ Determine the amplitude of the absolute displacement of the automobile mass.