CONICAL PENDULUM
If the bob of a simple pendulum is pulled to a side and whirled to move along a circle in horizontal plane, the string sweeps a cone and this arrangement is called conical pendulum.
If I is length of the pendulum, F is tension in the string,r is radius of the horizontal
circle and \(\theta\) is the semivertical angle of the cone, then
\(
\begin{gathered}
F\sin \theta = mrw^2 \hfill \\
F\cos \theta = mg \hfill \\
\tan \theta = \frac{{rw^2 }}
{g}and \hfill \\
w = \frac{{\sqrt {g\tan \theta } }}
{r} \hfill \\
\end{gathered}
\)
Time period \(
T = 2\Pi \frac{r}
{{\sqrt {g\tan \theta } }} = 2\Pi \sqrt {\frac{h}
{g}} = 2\Pi \sqrt {\frac{{l\cos \theta }}
{g}}
\)
(from r=lsin\(\theta\))..