A smooth rigid rod shown in the figure is attached to a table T that rotates in the horizontal plane about a smooth bearing at F

A smooth rigid rod shown in the figure is attached to a table T that rotates in the horizontal plane about a smooth bearing at F . The table has mass M , radiu s of gyration K about F, and its variable angular speed due to an applied driving torque I1F(t) = I1F(t)k about F is wet ) = e(t ). The mass of the rod is negligible. A slider block of mass m, supported symmetrically by identical springs of stiffness k, is released from rest relative to the rod at a distance a from the unstretched state at O . (a) Derive the equations of motion for the system (i) by use of Lagrange 's equation s, and (ii) by use of the Newton-Euler laws. (b) Find the torque I1F(t) required to sustain a stable motion of the system with a constant angular speed.

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