An object attached to a spring undergoes simple harmonic motion modeled by the differential equation

$m\frac{d^{2}x}{d{t}^2}+kx=0$ where $x(t)$ is the displacement of the mass $($relative to equilibrium$)$ at time $t,m$ is the

mass of the object, and $k$ is the spring constant. A mass of $6$ kilograms stretches the spring $0\mathrm{.}25$ meters.

Use this information to find the spring constant. $($Use $g=9\mathrm{.}8$ meters$/$second ${?}^2)$

$k=$

The previous mass is detached from the spring and a mass of $17$ kilograms is attached. This mass is

displaced $0\mathrm{.}8$ meters below equilibrium and then launched with an initial velocity of $-1\mathrm{.}5$ meters$/$second$.$

Write the equation of motion in the form $x(t)=c_{1}cos(t)+c_{2}sin(t).$ Do not leave unknown constants

in your equation.

$x(t)=$

Rewrite the equation of motion in the form $x(t)=$Asin$(t+),$ where Do not leave

unknown constants in your equation.

$x(t)=$