$xy-$plane is rotating with constant angular velocity $$ around the origin as shown. Material point with mass m is moving on the plane with no friction. An attracting force towards the origin proportional to the distance from origin, $-k,$ acts on m $.=+yj$ is the relative position vector of $m.$ There are no other active forces.

Denote the relative time$-$derivative $($w$.$r$.$t$.$ the rotating plane$)$ with over$-$dot.

Express drift, relative and Coriolis acceleration components.

Write the equations of motion in relative coerdinates $x,y.$

Obtain a single equation for $z=x+iy$ where $i=\sqrt[\phantom{2}]{-1}.$

Take $m=k==1.$ Initial conditions:

$x(0)=y(0)=1,x^{}(0)=1,y^{}(0)=0$

Solve the z$-$equation and find the trajectory $x(t),y(t).$