. Early geophysical papers of the Society of Exploration Geophysicists. Petroleum; Prospecting. CALCULATION OF MOTION OF GROUND 89 7 they only agree from / = 0 to / = 1. We see that to obtain the actual motion of the ground it is necessary to use a much longer period with a critically damped seismograph than with an undamped one. Fig. 8 shows the curves for x and — y when co = p — k so that the periods of the waves and of the seismograph are equal. The equations for x and y in this case are x = 1 - cos (300° y = - h sin (30/)° + (7r//12)e-"/6. The seismograph is less sensitive and x and —
. Early geophysical papers of the Society of Exploration Geophysicists. Petroleum; Prospecting. CALCULATION OF MOTION OF GROUND 89 7 they only agree from / = 0 to / = 1. We see that to obtain the actual motion of the ground it is necessary to use a much longer period with a critically damped seismograph than with an undamped one. Fig. 8 shows the curves for x and — y when co = p — k so that the periods of the waves and of the seismograph are equal. The equations for x and y in this case are x = 1 - cos (300° y = - h sin (30/)° + (7r//12)e-"/6. The seismograph is less sensitive and x and — y do not agree as well as when the period of the seismograph is greater than that of the If the period of the seismograph is one third that of the waves and the damping critical then we may take x = 1 - cos (300° so that co = 7r/6 and k=r/2. The equation for y is then 1 5irt + 8 y = cos (30/ - 36-87)° -\ e-*«2. 10 100 Fig. 9 shows the curves for x and — \0y in this case. — lOy is plotted instead of — y because the maximum value of y is only one twentieth that of the maximum value of x. Comparing Fig. 9 with Fig. 7 we see that the deflections of a critically damped seismograph with period three times that of the waves are somewhat similar in form but about ten times larger than those of a critically damped seismograph with period one third that of the waves. It appears that, while in all cases the initial deflections are equal and op- posite to the motion of the ground, the only case in which this remains true approximately for more than a fraction of a wave is that in which the period of the seismograph is large compared with that of the waves and the seis- mograph is undamped. The ratio of the maximum value of y to the maximum value of x is about (&/(<&— n2) or if T is the period of the waves and T' that of the seismograph it is T'*/(T'2—T^). This is equal very nearly to unity when T'/T is large and is nearly equal to (T'/T)z when T'/T
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