13For the second eigenvector (the symmetric mode, j = 2) … Inserting 225174kmω−=into the first of the two homogeneous equations yields 1222724kkaka−−+=22123174aa+=Letting a12= 1, then a22= 1.781 (Thus, in the symmetric normal mode, the amplitude of the vibration of the second mass is 1.781 that of the first mass and in phase with it.) The two eigenvectors (Equation 11.4.13 and see accompanying Table) are … () (111111211coscos0.281aQta)1tδω=−=−δ−)2t122222221coscos1.781aa=−11.18 ()2Tmlmll2θφ=++±±±2coscoscosVmglmgllθφ−+For small angular displacements … 22122112mmLTVlllmglmgl2θθ =−≈+++−+− ±212,2dLLmlmlllmgldt1∂∂=++=−±012g++ =22,Lmlllmgldtφφ=−±0ll g
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.