IB Physics Motion in a Vertical Circle

A sheet of harder questions on a mass moving on a string in a vertical circle is given below.

  1. A mass hangs at rest on the end of length L. The mass is given a horizontal speed U and the maximum vertical height to which the mass rises is L. Find U.
  2. A mass hangs at rest on the end of length L. The mass is given a horizontal speed U. In its subsequent motion the string becomes slack and the mass hits the point of supprt of the string. Find the initial speed U.