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One of the more important problems in mechanics is the study of periodic motions, that is, motions which repeat themselves in regular intervals of time, called the period. An example of periodic motion which we hrNe already encountered is uniform circular motion, in which the velocity and acceleration of the body at a given angular position were always the same. If a particle was found at a given position at a time t, we could be sure that it would return to that position at time t + T later, where T was the period of the rotational motion. A body in uniform circular motion moves under the influence of a varying force, the centripetal force, which, though constant in magnitude, varies in direction. In general, an object moving in periodic motion must move under the influence of a varying force which is directed to some equilibrium position or to some neutral position. In uniform circular motion this position is the center of the circle.