604 SEISMIC METHODS [Chap. 9 



damped frequency factors (in the denominator of eq. [9-98a]) are 



^fo) = -T-, — 2 ^n^ (fd) = —2 



or 





(/ff) = 2/. ■ 2; ai^d (/d) = 



wg(l + n^) coo(l + no) ' 



where n^ is the tuning factor (= w/co^) for the galvanometer and no(= w/ojo) 

 the tuning factor for the seismometer. Therefore, eq. (9-98a) can be 

 greatly simplified by making the two tuning factors equal, that is, making 

 the natural frequency of the galvanometer equal to that of the seismo- 

 graph. Then the product of the frequency factors (fg) and (fd), multiplied 

 by CO in the numerator, is n /coo(l + n )", so that the over-all magnifica- 

 tion is 



0)0 (1 + n^r 



The function n/(l + n'^Y, given in eq. (9-98c), is shown in Fig. 9-109. 

 It has its maximum at 1/n = 0.577. When galvanometer and seismograph 

 frequencies are equal and both are critically damped, the response is 

 peaked at a frequency 1.73 times the natural frequency. Galitzin gives 

 an instructive example showing that one seismometer with a period of 12 

 seconds was peaked at a period of around 6.9 seconds, while another with 

 a period of 25 seconds was peaked at 14.5 when connected to galvanometers 

 of matched natural frequencies. For 0.7 critical damping the damped 

 frequency factors are 



(/ff) ~ 2 /.. . ~. and (fd) = -2 



'^ff\/l + n* woa/I -|- n* 



so that for equal frequencies of seismometer and galvanometer the over-all 

 dynamic response is given by 



0)0 (1 + w*) 



This curve is shown in Fig. 9-109. The over-all magnification is greater 

 (less damping), the curve peak has moved closer to the tuning factor of 1. 

 The maximum is at 1/n = 0.77, that is, for a detector and galvanometer 

 which have equal natural frequencies and are 0.7 critically damped, the 

 over-all peak occurs at 1.3 times their natural frequency. Conversely, a 

 linear response may be produced by making the galvanometer frequency 

 a multiple of the seismometer frequency. Then, for 0.7 critical damping. 



