This problem was contributed by Gert Hamacher.
An accelerometer is made of a piece of wire with a bead on it that can slide on the wire with no friction. The wire is formed as a parabola y = kx2, as shown in the drawing. The bead rests at the lowest point of the parabola when it is at rest. When accelerated parallel to the x-axis the bead will climb up some on the wire. Find the relationship between the acceleration a of the wire and the bead’s maximum horizontal displacement x relative to the wire.
Answer :
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