A bob of mass m is suspended from a fixed point with a massless string of length L (i.e., it is a pendulum). You are to investigate the motion in which the string moves in a cone with half-angle ?.

a. What tangential speed, v, must the bob have so that it moves in a horizontal circle with the string always making an angle ? from the vertical? Express answer in terms of some or all of the variables m, L, ?, and free-fall acceleration g.

b. How long does it take the bob to make one full revolution (one complete trip around the circle)? Express answer in terms of some or all of the variables m, L, ?, and free-fall acceleration g.