()2Lmkx lmgx′∂=−−++∂32mmmxkxlm′′+=−−++±±gFor 2gmyxlmk′=−−+, 03mmyky′++=The block oscillates about the point 2xlmk′=++… with a period … 232mmkπωT′+==D10.17Note: 4 objects move – their coordinates are labeled ix: The coordinate of the movable, massless pulley is labeled px. Two equations of constraint: ( ) ( )111,0ppfxxxlx=−− =( ) ( ) ( )2232 3,,20fxxxx xx l′=+− +=222112333111222LTV mxmgx mgxmgx=−=−+−+−±± ±30jjjiiifLdLqdtqqλ∂∂∂−∂∑Thus: (1) 110mg−− +=(2) 220mg mx(3) 320Now – apply Lagrange’s equations to the movable pulley – note 0pm→So: (4) 120ffxxλλor20−=Now - pxcan be eliminated between
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.