124 K. YE. Veselov and V. L. Panteleyev 



paper (2) given that only the vertical disturbing acceleration, which is sinu- 

 soidal in character, is acting, that the angles of deviation of the pendulum 

 from the equilibrium position are small and that the damping is propor- 

 tional to the speed at wliich the pendulum moves. 



In this case the equations for forced and natural motion take the form: 



ml 



6>i = —=r- .:.= sin {pt + d), (1) 



l/(7Zo2-/>2)_4£2^2 



(92=^^-^(aie-«=f-a,e-«^0 (2) 



where % and a2 are the roots of the characteristic equation {a^ — — e+)/e^ — tZq, 

 a2 = — £ — Ke^ — /?q); Uq is the natural oscillatory frequency of the pendulum 

 without damping ; / is the moment of inertia of the bar in the system ; mla^ 

 cos [pt) is the moment of the disturbing force, on the assumption that the 

 disturbing acceleration is sinusoidal in character; h is the damping coeffi- 

 cient ; K is the torsional rigidity coefficient of the elastic element ; p, a^ are 

 the amphtude and frequency of the disturbing acceleration; 



— = riQ^, — = 2e. 



It follows from formula (1) that, under the influence of sinuspidal disturb- 

 ing accelerations, the bar will also accomplish sinusoidal forced vibrations. 



ml 

 If the value of the static amplitude d = 2 a^ be divided by the value 



for the dynamic amphtude obtained from equation (2), we obtain the dynamic 

 coefficient (in paper (2) a value which is the reciprocal of the dynamic 

 coefficient is named the coefficient of interference suppression). 



1 = , . (3) 



Where A, the dynamic coefficient, shows the decrease in the oscillatory 

 amplitude of the gravimeter bar under the influence of sinusoidal accelera- 

 tion of a given frequency compared with the constant acceleration of the 

 same frequency. 



The dynamic coefficient is necessary firstly in order to know the ampli- 

 tude and frequencies of the disturbing acceleration at which measurements 

 can be made, and secondly to find the amphtude of the vertical component 



