A mass $(m=4\mathrm{.}31kg)$ is connected to a spring $(k=182\mathrm{.}4\frac{N}{m})$ on the surface of a horizontal, frictionless table and constrained to move in the hat$(j)$ direction $($gravity is pointed in

the hat$(k)$ direction$).$ When displaced from equilibrium, the mass enters into simple harmonic motion. Take the equilibrium location of the mass to be the origin.

At time $t=0s,$ the mass is observed to be displaced from equilibrium to vec$(r)=0\mathrm{.}484$mhat$(j)$ and traveling with a velocity vec$(v)=2\mathrm{.}175\frac{m}{s}$hat$(j).$

$($The following questions will be marked correct only if your answer is within $1\%$ of the correct value.$)$

What is the position of the mass at time $t=1\mathrm{.}208s?$

mhat$(j)$