Lagrangian Dynamics - bead on wire

I have a bead on a wire that is at an angle to the vertical, I need to show that there is a starting distance along the wire where the bead will exhibit circular motion regardless of the radius.

Working in spherical polars I get the equation of motion as

mr''=mr(wsin(a))^2-mgcos(a)

which yields

r=A(e^wsin(a)t)-B(e^-wsin(a)t)+(gcos(a)/(wsin(a))^2)

I have been asked to show that for r0=gcos(a)/(wsin(a)) the particle exhibits circular motion. However, I get a hyperbolic function - which is correct for other starting conditions... and can't show that r'=0...

Any help appreciated. Thanks.

could you post the full question please? it's not clear to me what you mean/what the variables are.

could you post the full question please? it's not clear to me what you mean/what the variables are.

here?

you are pretty much there. note that they gave you initial conditions.

solved it - question was wrong... now stuck on 3c...

The trick is to notice that the second system is not inertial so you have to modify N2 when treating it.