HW $14$ Higher$-$Order Linear Models: Problem $1$

$(1$ point$)$ A brick of mass $6$ kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by $9$ cm $.$ The spring is then stretched an additional $3$ cm and released. Assume there is no air resistance. Note that the acceleration due to gravity, $g,$ is $g=980c\frac{m}{s^2}.$

Set up a differential equation with initial conditions describing the motion and solve it for the displacement $s(t)$ of the mass from its equilibrium position $($with the spring stretched $9$ cm $).$

$s(t)=$

$$ cm

$($Note that your answer should measure $t$ in seconds and $s$ in centimeters.$)$