Chap. 9] 



SEISMIC METHODS 



581 



\ToJ r' 



(9-82a) 



where To is the natural period of the pendulum, g is gravity, l' is pendulum 

 length, and J is indicator length. If h is the deflection of the mass from 



TABLE 59 



its rest position and a the corresponding ampli- 

 tude of the pointer, the indicator or static mag- 

 nification is 



V = - = 



/' 



(9-826) 



-ad^'" 



\wQ COSf 



% 



If the suspension point of a seismograph is dis- 

 placed rapidly, the ground displacement is recorded 

 with the magnification V in opposite direction, 

 and the negative indicator magnification gives the 

 pendulum displacement for rapid ground move- 

 ments. In the corresponding physical pendulum 



the period is proportional to the distance of the center of oscillation from 

 the axis of rotation. The reduced or equivalent pendulum length is given 

 by 



Fig. 9-96. Seismometer 

 as a pendulum. 



= '(£) ■ 



(9-82c) 



Substituting, in eq. (9-82c), coo for 27r/J'o , where wo is the angular 

 frequency of the seismograph, hereafter briefly referred to as natural 

 frequency, (coo = 27r/o, see eq. [9-1 8a]), 



2 



«o = 



mg% 



(9-82d) 



where s is the distance of the center of gravity from the axis of rotation 

 and K the moment of inertia about the same axis. For any type of 

 spring seismograph, 



^g 



m d' 



2 

 Wo 



(9-83) 



