I did

$\displaystyle \tan \theta = \frac{r}{h}$ where r is the radius

so $\displaystyle h \tan \theta = r $

$\displaystyle T \cos \theta = mg$ where T is the tension

$\displaystyle T = \frac{mg}{\cos \theta}$

using the standard circular motion result

$\displaystyle T \sin \ theta = m \omega ^2 r $

$\displaystyle mg \tan \theta = m \omega ^2 h \tan \theta$

giving $\displaystyle \omega^2 = \frac{g}{h}$

where did i go wrong ?