333 



elastic recovery is given by 



(12) 



where the time "t^ of deflection is detennined by the condition that the 

 derivative &(fr»») of G vanish. 



If i/fCo) of Eq. (9) is eaqpanded in powers of c"***^*- and C 

 is chosen greater than the greatest real part of the roots u?^ of 



F.('^k)'°, to) 



it may be shown that for t < ©^ , the deflection ■x.^L-i) is given by Eq, (11), 

 except that the sum extends over the zeros of F^ (uj^ rather than over those 

 of FC^; . 



If, on the other hand, e'**'^* is expanded in powers of «; e^ 

 and terms of the order u> ** are neglected, FCw^is approximated by the ex- 

 pression 



^^ '- O.Xi^T , [ (14) 



^ ( Mg5 \ '/>- 



Eq, (14) represents the incompressive approximation to F(u?P , in vrtiich the 

 apparent plastic frequency u>* differs from that of the free plate due to 

 the loading effect of the water. When % &^ is s;iiall relative to unity. 



24 



