# Weight And Springs

In the $$xyz$$-coordinate system, there are 4 fixed (immovable) points at $(x,y,z) = (\SI{1}{\meter},\SI{0}{\meter},\SI{0}{\meter}),\ (\SI{0}{\meter},\SI{1}{\meter},\SI{0}{\meter}),\ (\SI{-1}{\meter},\SI{0}{\meter},\SI{0}{\meter}),\ (\SI{0}{\meter},\SI{-1}{\meter},\SI{0}{\meter}).$ There is a movable $$\SI{1}{\kilo \gram}$$ mass attached to each of the 4 fixed points by a spring of spring constant $$k = \SI{1}{\newton \per \meter}$$. The mass is initially at rest at $$(x,y,z) = (\SI{0}{\meter},\SI{0}{\meter},\SI{0}{\meter})$$, and the springs are initially un-stretched.

The mass falls under the influence of gravity $$\big(\SI{10}{\meter \per \square \second}\big)$$ in the $$-z$$ direction of the springs. When air resistance eventually brings the mass to rest at an equilibrium position, how far (in meters) is the mass from the origin (to 2 decimal places)?

Note: All quantities are in standard SI units.

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