Damped Oscillation 12-19-2020 (Part 1)

A block of mass $m$ is connected to one end of a spring of force constant $k$ and natural length $L_0$ . The other end of the spring is fixed in place at the origin $(x,y) = (0,0)$ . At time $t = 0$ , the block is at position $(x,y) = (1,0)$ with velocity $(\dot{x}, \dot{y}) = (10,10)$ . The ambient gravitational acceleration $g$ is downward, which corresponds to the $-y$ direction. As the block moves, it is subjected to damping forces, such that the total force on it is:

$\vec{F} = \vec{F}_s + \vec{F}_g + \vec{F}_D \\ = \vec{F}_s + \vec{F}_g -D \vec{v}$

In the above equation, $\vec{F}_s$ is the spring force exerted on the block, $\vec{F}_g$ is the gravity force exerted on the block, $\vec{F}_D$ is the damping force exerted on the block, $\vec{v}$ is the velocity of the block, and $D$ is a damping constant.

When the block comes to rest in its equilibrium position, how far away is it from the origin?

Details and Assumptions:
1) $m = 1$
2) $g = 10$
3) $k = 5$
4) $L_0 = 1$
5) $D = 0.5$
6) Assume standard $SI$ units for all quantities