. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. Waves due to a floating sphere making heaving oscillations 6 On the sphere we have 4> = aL'{C cos at + D sin at) + n^aJoi/ism 6) e-l^''°^''(G sin o-t-D cos at) + i;«{inP2n-M) + P2nW] (^« ^os at + B,sin at), (29) where, after using (21), (23) and (25), L' = l-i77yJe-/'«°««{/fo(yffsin^) + 7o(yffsin5)}-/?^e-Acos9. We obtain Z in the form Z = ^npa^ka sin at — ^7Tpa^2ha cos at, with ^k = L[C-7r/]M[D + {^/3 + ^)A^-igA^ + ^As-..., §h = L[D + 7T^M[C + {^/i + l)B,^^B, + j^B,-.... In (32) and

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. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. Waves due to a floating sphere making heaving oscillations 6 On the sphere we have 4> = aL'{C cos at + D sin at) + n^aJoi/ism 6) e-l^''°^''(G sin o-t-D cos at) + i;«{inP2n-M) + P2nW] (^« ^os at + B, sin at), (29) where, after using (21), (23) and (25), L' = l-i77yJe-/'«°««{/fo(yffsin^) + 7o(yffsin5)}-/?^e-Acos9. We obtain Z in the form Z = ^npa^ka sin at — ^7Tpa^2ha cos at, with ^k = L[C-7r/]M[D + {^/3 + ^)A^-igA^ + ^As-..., §h = L[D + 7T^M[C + {^/i + l)B, ^^B, + j^B, -.... In (32) and (33) we have put L[=rL'P^(/i)dju, , M[ = ( Jo{^sine)e-^'=°^^P^(/i)d/i. (34) Jo Jo The velocity of the sphere being cos at, the first term in (31) represents an addition to the eflFective mass, the virtual inertia coefficient being k as given by (32), The (30) (31) (32) (33) 0-8-. FiOTTBE 1. Variation of virtual inertia coeflRcient k and damping parameter 2/i with frequency second term in (30) being proportional to the velocity, the quantity h as given by (33) may be caUed a damping parameter; it gives some estimate of the damping factor if the motion were unforced damped periodic motion. We may obtain an 607. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original work.. Havelock, Thomas, Sir, 1877-. Washington, Office of Naval Research, Dept. of the Navy; for sale by the Superintendent of Documents, U. S. Govt. Print. Off