$(15$ points$)$ Earthquakes cause ground oscillations at frequencies below the range of human hearing, that is below $20$ Hz$.$ Suppose an earthquake caused a building to oscillate in simple harmonic motion horizontally at f $=12$ Hz$.$ A desk in this building has a coefficient of static friction, $=0\mathrm{.}8,$ with respect to the floor. a$)$ What is the largest amplitude of motion such that the desk does not slip on the floor? A $=0\mathrm{.}00137$ m b$)$ At this amplitude, what is the resulting maximum velocity? vmax $=0\mathrm{.}104$ m$/$s