Here I consider the motion of a particle attached to a light inextensible string moving in a vertical circle and discuss the motion, methods and the equations that can be formed.
I also look at motion when the string becomes slack.

Motion in a vertical circle - particle on a string : ExamSolutions Maths Revision - youtube Video

String goes slack

Motion in a vertical circle - Particle on a string when it goes slack : ExamSolutions Maths Revision - youtube Video