276 .30- 



Substltuting b = b In (3.2), we get 



(3.6) 



_yi -a^ - ka-V^ 



^^/^ /r7 



The solution of (3.6) Is immediately obtained by integra- 

 tion, with the following result for the half -period t, : 



(3.7) t^ = / ■'■dt = / ■■■ ^ 



^1 ^'^'/^^^^ 



^l-a^ -ka-V4 



da 



where a is the smallest and a, the largest root of 



(3o8) 



1 - a"^ - k a 



-3/4 _ 



0. 



To evaluate the integral (3.7) it is necessary to 

 have a specific value for k. The value of k is given 

 by (2.10) and depends on the distance D of the explosion 

 from a point 33 ft. above sea level. The following table 

 is calculated from (2.10): 



Selecting a depth of water of about 100 ft. as typical, 

 the value of k is approximately .2. We shall select this 

 value of k throughout the remaining calculations. A differ- 

 ent value for k will change the formulas slightly. 



For k = .2, the roots a , a, of (3.8) are 



(3.9) 



a^ = .118, 



a^ = .924. 



