334 



it may be verified that ± cu?^ closely approximate two of the zeros of 

 the exact F(u>) of Eq. (9). With the neglect of other zeros of FCu>^ , we 

 obtain the complete incompressive solution from Sq. (ll)l 



:r,a;= 2^-^:_^[^c.»t.u,fete-'5/^-c^u,*0]. (15) 



Using Eq, (12), vre finally obtain for the maximum deflection and duration 

 of deflection 



t^ - <!>/<^t i f (16) 



^.(»/«o/0 



When co*0 is small relative to unity, p is approxuiated by tt/x , 

 the deflection is proportional to the momentum of the incident wave, and the 

 duration "fc^ equal to one-fourth the plastic period xir/tJp* of the loaded plate. 

 When u?^ © is large relative to unity, a** (» is approximated by i/u^*"© , 

 the deflection becomes proportional to the peak pressvire, and the duraticxi 

 equal to the half-period. Thus a diaphragn gauge vrfiich measures momentum 

 for small charges might well measure peak pressure for veiy large charges. 



It is of interest to put Eqs. (l6) in a more convenient form for 

 numerical use. We denote by I the impulse b^ © of the incident wave in 

 p si-milliseconds, and we express the yield stress a~ in ^si^ and the densi- 

 ties p^ £ind p of water and plate in grams/cm3. With these units, Eqs. (l6) 



25 



