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APPENDIX B 

 DETAILS OF THE SOLUTION IN SECHON 2, PART IV 



The equation of motion (3)> Part IV, to be solved is. 



where 



and is an integral, operator defined by 



Eq. (B-1) is most conveniently solved by the method of Laplace transforms. 

 Taking the Laplace transform of both sides, we get 



CoM\^AO)l(tc,u,) -u?J>-^^(x^LCx,«o))= tl^\ (B-2) 

 where 



and 



If the deflection z6f^t} ^^ expanded in a series of Bessel func- 

 tions as in Eq. (5), Part IV, 



where J^ Cu-) is the zero order Bessel function of w. , and K^ is the i-th zero 



96 



