Not as usually, oscillation

Body of mass $m$ is moving around frame in the shape of Г. The frame is rotating about point O with a constant angular velocity $\omega$ in the vertical plane. The body is attached to a point A with an spring of a coefficient of elasticity $k$ . Find the amplitude $X_0$ of the oscillations.

$g=10$

$k=8$

$m=2$

$\omega=1$