Question

To register the verticals vibrations, we use the instrument that is show in the figure 23, in which a rigid framework AOB, who carries the weight W,

can rotate around an axis that passes through O and it is perpendicular to the plane of the figure. Determine the frequencies of the small verticals vibrations if the moment of inertia 1 of the frame plus its weight, with respect to the axis passing through O and the spring constant k are known and all dimensions are given.

od za SB Fig. 23

Answer 1

Date: sau Cosx In equilibrium position there is initial tension of the spring which balances the weight w in a - / B ao (osmall) ow particular position. So, we give anguiare displacement o about this equilibriunion For the fixed point '0' we can write Torque about 6 - Io x = I, {where Is is the combined moment of inertia of the frame AOB along with the Weight W ? . We have, Io ő = - k a a O = of kar o=0 - cos a I. Cosa We have ö tun?o=0 2 w Kamin wa' natural frequency Y Io cosa the system?