ANSWERSLagranges method (Energy Method)a)( )()+() = Where xi= generalized coordinatesT= Total Kinetic Energy of the systemU= Total Potential Energy of the systemQi= External forces momentsFrom the system;111 12 + 22 + 3222211111 = 12 + (2 1 )2 + (3 2 )2 + 32 + (3 1 )2222221 2+ 22= = ( )= = =0 = 01st coordinate at xi = x1 () = 1 1= 1 + 1 2 + 1 3 = 1 (3) 2 312nd coordinate at xi = x2 () = 2 2= 2 1 + 2 3 + 2 = 1 + 2 (3) 323rd coordinate at xi = x3 () = 3 3= 3 2 + 3 + 3 1 = 1 2 + 3 (3)3b) 1 + 1 (3) 2 3 = 0 2 1 + 2 (3) 3 = 0 3 1 ...

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