Question

Problem 3: [2, 03-15] A rigid and uniform bar undergoing rota- tional motions in the vertical plane is re- strained by a torsional spring of stiffness k at the pivot point O, as shown in the figure. The bar has mass m and a length& and the torsional spring is unstretched in the upright position a) Find the equations of motion, lin- ke earized about 6 0: b) Determine what ke should be so that small oscillations about the upright po- sition of the bar are stable; c) Rewrite the (second-order) equation of motion as a pair of first-order differen- tial equations.

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Answer 1

Answer:

Given that:

   A rigid and uniform bar undergoing rota- tional motions in the vertical plane is re- strained by a torsional spring stiffness $K_{t}$ and the Pivot point O.

1 Ag: toa onal Spring 9-o: iven Topce & urin about 0 3 2- mi' 2

ba ae Stable: Stable ven ot' le Can ge 3 2