Cooridinate+Mechanics

A piece of wire is bent in the shape of a parabola whose equation is $y=kx^2$ ( $y$ -axis veritical) with a mass $m$ on it. At rest, it stays on lowest point of the parabola. The wire is now accelerated parallel to $x$ -axis with $a$ . What is the distance of new equilibrium position of the mass from the $y$ -axis, where it can stay at rest with respect to wire?

Details and assumptions:

• Assume the system to be smooth (frictionless).

• Acceleration $a$ is constant.