In the woods at Basildon Park near Reading we found this odd skittles game. There was a central pole with a mass on the end of a string that can go round. The trouble was that the string was too short to let the mass reach the skittles.
It was, though, a nice example of a conical pendulum.
The real forces are shown in blue. Weight W=mg downwards and tension along the string. They are not balanced so a resultant force acts. It is a centripetal resultant force as shown in red. The mass accelerates towards the centre of the circle. Vertically, mg = Tcos(theta). Horizontally centripetal force m.vsquared/radius = Tsin(theta). If you put the two together and cancel T, you get vsquared = gr.tan(theta). If the string has length L, then tan(theta) = r/sqrt(Lsquared - rsquared).
