# Spring Compressed on Parabola

Two $$\SI{1}{\kilo\gram}$$ beads are at the ends of a compressed spring resting on a smooth parabolic wire $$\big(y = x^2\big).$$ The spring has a natural length of $$\SI{1}{\meter}$$ and a force constant of $$\SI[per-mode=symbol]{5}{\newton\per\meter}.$$

If the system is in static equilibrium, how far away from the $$y$$-axis is each bead (in meters)?

Note: The spring is horizontal and gravity is $$\SI[per-mode=symbol]{10}{\meter\per\second\squared}$$ in the $$-y$$ direction.

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