Solution - Spring and Hanging Ball

If the ball is in equilibrium position, total forces works on the ball equals to zero,

The ball is then brought to an arbitrary position, so its position vector is

Hence, the total forces works on the ball are

Substitute from equation (1), and we can get

From the picture above, we can conclude that this system is the same as a system with a spring attached to the ball's equilibrium point without gravitational force.
Because in the new system there's no gravity, we can conclude that the highest position of the ball is at the other side, point A (see picture above).

Substitute and from equation (1) and (2) to equation (5),

And now we can get the coordinate,

That's my solution.
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Thank you.