Identify the generalized coordinates and the number of degrees of freedom of the log.

Identify the generalized coordinates and the number of degrees of freedom of the log. Use Lagrange’s method to deduce the equations of motion and thus determine the frequency of the vertical oscillations of the log. The wire and bob assembly of the rotating simple pendulum shown in the diagram for is replaced by a thin rigid rod of length I and mass m. The rod is hinged in a smooth bearing at 0 and is free to slide on the smooth horizontal table.

(a) Identify the rheonomic constraint and apply Lagrange’s equations to derive the equation for finite amplitude oscillations of the rod relative to the table.

(b) Relax the constraint, determine the generalized forces that act on the rod at its hinge bearing, and thus find the constraint reaction force as an exact function of the finite angular placement fJ for initial data fJ(O)= fJo and ~(O) = O.

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