A classical mechanics problem involve rotating

[drop_out_kid]

Homework Statement

I intuitively think this is a helix, x(t) probably a exponential solved by ODE, but I cannot come up with it.. I think in this problem. Coriolis force is for tangential acceleration(r(t) increases) and the centrifugal force is making r(t) increases.

Relevant Equations

F_cor=2mv $Omega$
F_cf=$Omega^2$m*r

I came up with these: (especially not sure if second is right)

 

[drop_out_kid]

From eqs 1 I can get r is exponential, question is to get y/x or other relation from eqs 2

 

[haruspex]

Homework Statement:: I intuitively think this is a helix, x(t) probably a exponential solved by ODE, but I cannot come up with it.. I think in this problem. Coriolis force is for tangential acceleration(r(t) increases) and the centrifugal force is making r(t) increases.
Relevant Equations:: F_cor=2mv $Omega$
F_cf=$Omega^2$m*r

View attachment 300109

I came up with these: (especially not sure if second is right)
View attachment 300110

The instructions are to use x as the radial distance, etc. Turning those into r, phi and using x, y for fixed axes is not going to help.
Start by considering first derivatives, like $\dot y$.