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what determine whether a pendulum swings in a plane or describes a three dimensional plane
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Its initial velocity! If the plane containing the line from the pivot to pendulum and the velocity vector also contains the gravitational force vector is vertical, then the motion of the pendulum will be confined to a vertical lane. this is because no force acts on the pendulum that can bring it out of that plane - the force of gravity is vertical, and is contained within the vertical plane.
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