# Cheap swing-set

An inexpensive swing-set is made of two vertical poles with a connecting beam attached to the tops. The swing is hanging from the center of the connecting beam.

Due to the slight bending of the vertical poles the hinge points of the swing, that are fixed to the beam, are not entirely motion-less. As a child uses the swing the connecting beam will have a slight motion in the horizontal direction. When the seat is in the forward direction, the beam is pulled a bit forward and when the seat is in the backward direction, the beam is a bit backward, too.

In the figure here the top (black) curve represents the angle of the swing relative to the vertical, as a function of the time. The other four curves represent the horizontal position of the connecting beam, as it responds the the motion of the seat. When the swing is used vigorously, which one of the curves represents best the position of the connecting beam?

Assume that the mass of the beam (and the poles) is much smaller than the mass of the child that uses the swing.

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