Expression of conical pendulum prove it

The time period of a conical pendulum is directly proportional to the square root of its length. The time period of a conical pendulum is directly proportional to the square root of the cosine ratio of the semi-vertical angle that is the angle made by the string of conical pendulum with the vertical.

This is called a centripetal force. The equation for centripetal force is Fc = mv 2 /r, where m is the mass of the object, v is the tangential velocity, and r is the radius of the circular path.