Q$11.$A $0\mathrm{.}400-kg$ block oscillates up and down on a vertical spring for which $k=12\mathrm{.}0\frac{N}{m}.$ The initial amplitude of the motion is $0\mathrm{.}1$ m $.$

$($a$)$ What is the natural angular frequency $?$

$($b$)$ If the observed angular frequency is ${}_d=3\mathrm{.}89s^{-1},$ what is $b?$

$($c$)$ Write an equation for the position as a function of time.