458_Physics ProblemsTechnical Physics

458_Physics ProblemsTechnical Physics - 460 P15.57...

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460 Oscillatory Motion P15.57 (a) L i a a L h FIG. P15.57(a) (b) T L g = 2 π dT dt gL dL dt = 1 (1) We need to find Lt af and dL dt . From the diagram in (a), LL ah i =+− 22 ; dL dt dh dt =− F H G I K J 1 2 . But dM dt dV dt A dh dt == ρρ . Therefore, dh dt A dM dt 1 ρ ; dL dt A dM dt = F H G I K J 1 2 (2) Also, dL A dM dt tLL L L i i z = F H G I K J F H G I K J 1 2 (3) Substituting Equation (2) and Equation (3) into Equation (1): dT dt g a dM dt i a dM dt = F H G I K J F H G I K J + 1 2 1 2 1 2 2 ch . (c) Substitute Equation (3) into the equation for the period. T g L a dM dt t i =+ F H G I K J 21 2 2 Or one can obtain T by integrating (b): dT g a dM dt dt TT
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