94 H. A. WILSON 
asin pt + op f { f sin pra at 
0 0 
ws 
which gives 
— x =asinpt+ ofc — cos pt)dt 
0 
so that 
— x = asin pi+ pat — asin pt = pat. 
Thus in this case the ground moves with uniform velocity ap. The sudden 
starting of this motion at t=0 starts the seismograph oscillating freely with 
amplitude a but has no further effect on the motion. If a ground wave ar- 
y 
OM 2 4 
0 
k=O, T=7/2 

Fig. 16. 
rives the period of which is long compared with that of the seismograph it 
will produce a nearly uniform motion of the ground for a short time which 
will start the seismograph oscillating with its natural period. 
238 
