598 SEISMIC METHODS [Chap. 9 



the amplifier by transformers which are inefficient in the range from to 

 20 cycles. Therefore, the response of a seismograph amplifier rises with 

 frequency in this range. Depending on interstage coupling, some ampli- 

 fiers have an essentially straight response, others keep rising in the range 

 up to a hundred cycles, and still others are peaked. Peaking may be 

 accomplished by filters or by resonant circuits. In view of these differ- 

 ences a general and approximate solution only may be given. The re- 

 sponse may be considered equivalent to one obtainable by assuming a 

 definite damping factor and a natural frequency approximately equal to 

 the peak frequency. 



In the steady state the general equation for the amplitude of a force- 

 coupled system is 



U = ^a ,— ^ • Y sin (coi - ^), (9-95) 



^// 2 2n2 , . 2 2 



where Va is the equivalent magnification or gain of the amplifier, Wa its 

 equivalent natural frequency, €„ the equivalent damping, y the output 

 (current), and Y the peak value of the input voltage. As is shown below, 

 the above expression fits the experimental results, although its simplified 

 form is equivalent to disregarding the action of input and output devices. 



3. Galvanometer. Three types of galvanometers (Fig. 9-106) may be 

 employed in seismic recording channels: (a) oscillographs, (b) coil galva- 

 nometers, and (c) string galvanometers. All have in common a magnetic 

 field and a current-carrying conductor in this field. In a string gal- 

 vanometer only one conductor is present; its motion in respect to the 

 lines of force is transverse. In coil galvanometers and oscillographs, two 

 conductors are traversed by currents in opposite directions so that a rota- 

 tional motion results. 



In an oscillograph, assume a bifilar loop to be suspended in an air gap 

 of the length L of a magnet with the field strength H^ . The distance of 

 the wires or ribbons is 2d; its plane of rest is parallel with the lines of force; 

 T is the equivalent torsional coefficient of the suspension; K the moment 

 of inertia of the wires inclusive of that of the mirror; and <p the deflection. 

 Then the equation of motion for free oscillation is Kip -\- T(p = 0. For the 

 deflection cp produced by a current 7, the torque is — 21101 Ld cos <p. Since 

 2Ld is the area S of the loop between the pole pieces, the current torque 

 is — H„S7 cos <p. In the equihbrium position this is balanced by the 

 elastic torque of the suspension T<p, so that for static deflections t(p = 

 HS7 cos (p. For small angles cos (p = 1, so that the equilibrium of elec- 

 trical, elastic, and inertia forces in the state of oscillation is given by 



Kip-\- T<p = HS7. (9-96a) 



