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A bead of mass m can move without fricti...

A bead of mass m can move without friction along a long wire bent in a vertical plane in the shape of a graph of a certain function. Let `l_(A)` be the length of the segment of the wire from the origin to a certain point A. It is knonw that if the bead is released at point A such that `l_(A) lt l_(A_(0))`, its motion will be strictly harmonic `l (t) = l_(A) cos omega t`. Prove that there exists a point `B (l_(A_(0)) lt lt l_(B))` at which the condition of harmonicity of oscillations will be violated.

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