CALCULATION OF MOTION OF GROUND 91 
which gives 
2Aw* 
me skie 
. uF , 
sin — sin w(t — w/w). 
w? — p? w 
From t=0 to t=27/w the equation for y is 
Aw? 
y= aces wt — cos pt) 
w?— p 
as for x = A(1—cos wt) when ¢>G. 
The curves for y and x in the three cases 
AG —wlemnco—n7/ OF = 1/18 
A Sil, ® = 6, = 1/6 
A=1, w=r7/6, = 7/2 
are shown in Fig. 10, Fig. 11, and Fig. 12. 

Fig. 10. 

Fig. 11. Fig. 12. 
In Fig. 10 the period of the seismograph is three times that of the wave 
and a large oscillation is started in the seismograph. In Fig. 11 the two periods 
are equal. In Fig. 12 the period of the seismograph is one third that of the 
wave and the wave ends with the seismograph in equilibrium so that y=0 
after the wave has passed. 
Now suppose that the seismograph is critically damped so that ».=0 
and k=p. In this case the equation for y when ¢>27/w is of the form 
y =a+b(t—2/w)e-*(t-2"/*) and the curves from ¢=0 to ¢=27/w, of course, 
are the same as with x = A(1—cos wt) when ¢>0. Figs. 13, 14 and 15 show the 
curves for —y and x in the three cases 
235 
