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Figure 6-43 shows a "conical pendulum", in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.060 kg, the string has length L = 0.90 m and negligible mass, and the bob follows a circular path of circumference 0.90 m.
What is the period of the motion? The tension in the string is 0.596N.
The half-angle at the apex of the cone is theta = sin^-1[0.9/2 pi)/0.9]
= sin^-1(1/2 pi)
= 9.1 degrees
for the period of a conical pendulum. At this rather small cone angle, the period will be nearly the same as that of a normal pendualum of the same length.
4sin^2(theta) - 2sin(theta) - 2 = 0 on the interval 0 (less than or equal to ) theta < 2(pi)?