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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1 solution
The beam responds to the horizontal component of the tension force in the ropes/chains that hold the seat. As long as the mass of the beam is small, the displacement will be proportional to this force F x .
It is clear that F x = 0 when the rope/chain is vertical. That excludes "C" and "D". "A" would be a simple answer, but only if the angles are small. In a typical swing motion the angle can easily reach 45 - 60 degrees. In that case we have to consider the fact that the tension force itself is reduced when the angle is large (it would reach zero when the angle is 90 degree). Therefore the correct answer is B.
NOTE: I have a slightly more elaborate swing set at home that exhibits this same phenomena. This problem is based on real observation!