The dynamics of the double-pan beam balance

The dynamical behaviour of the double-pan beam balance is investigated for the case of free vibration and also for the case of forced vibration of the type that is commonly called ground vibration; this being motion which is coupled to the balance via its central pivot. Considered first is the case of free vibration in which the central pivot is stationary. Here the small-angle approximation is made, thus linearizing the equations of motion and resulting in normal-mode solutions. Secondly, the case of a balance subjected to ground vibration is studied. Here the complexities of non-linearity and forced vibration are considered and, although this situation is difficult, in certain special cases the equations of motion are shown to be amenable to algebraic analysis. In particular, non-linear behaviour in the special case of free vibration is investigated. Finally, the effects of parametric excitation are also studied. The results of this analysis suggest a feedback control of the beam balance which will, if realized in practice, isolate it more effectively from ground vibration than has been possible in the past.