590 Mr. D. Coster on the Rotational Oscillation 



boundary-condition a R = acospt, R being the radius of the 

 cylinder. We therefore assume that there is no slipping 

 along the wall. 



Hence » _ all 



Hf'(cR)' 

 so that 



«R Hr(er) . 



ipt 



^=E TT(2)/m -~~-e' (7> 



HW 



The symbol R means that the real part has to be taken of 

 the function which stands after it. 



If we had chosen for c the root with the positive imaginary 

 part, we should have had to utilize the function H^. It is 

 quite easy to verify that this would not have made any 

 essential change in the solution (7). 



For large values of x (real and positive) TLf\x \/ — i) 

 approaches asymptotically to 



therefore for (&R) sufficiently large : 



_ *L 

 aU e V2 / k x K 



where <£ = argH< 2) (cR). 



From (8) it appears that damped waves are propagated 

 from the cylinder to infinity, the velocity of propagation 

 being 



/c/v/2 k V p ' 



and the wave-length 



X= (! T=^ = 2 Y 2 =2^/^. . . . (80 



JO k V /?p V 7 



The frictional moment on the wall of the vibrating 

 cylinder is '27t/jlW ^— where a> = ^~ . First we determine 



L^J E £rom < 7 > : 



ra<i P r a ipl . Hf ( C r) M -\ 



