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A weightless horizontal rigid rod along ...

A weightless horizontal rigid rod along which two balls of the same mass m can move without friction rotates at a constant angular velocity `omega` about a vertical axle. The balls are connected by a weightless spring of rigidity k, whose length in the undeformed state is `l_(0)`. The ball which is closer to the vertical axle is connected to it by he same spring. Determine the lengths of the springs. Under what conditions will be balls move in circles ?

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