ps5 (1) - MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF OCEAN ENGINEERING DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING 13.013J/1.053J Dynamics and Vibration Fall 2002 Problem Set 5 Issued: Day 12 Due: 11am, Day 16 a) 4-59 b) 4-61 c) 5-5 d) 5-6 e) 5-7 f) Supplementary Problem 1, attached .The supplementary problem is intended to be solved by the entire class jointly. g) Self-Evaluation in another sheet as per the instructions in the first class. All students are supposed to work on all the problems assigned.
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Supplementary Problem 1 x g x(t) D m Figure 1 A rigid hollow negatively buoyant sphere of mass m with frontal area A and volume V is given an initial downward velocity v i at the surface of the ocean of depth D and water density ρ w . The fluid force on the sphere is given by . . .. F x (t) = − 1 ρ w c d A x x c m ρ w V x ρ w gV 2 where c d , c m are drag and added mass coefficients which are taken as constants, and frontal area A = π R 2 and volume V = 4 π R 3 / 3 , R
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