201201aanda==Thus, the normal modes are approximately … 0010iti teandeωΩQQNote that we could have guessed this almost immediately. The above assumption is tantamount to omitting the cross elements . This completely eliminates the small coupling between the two oscillators, which reduces the matrix to the purely diagonal terms … 2m−2−KM()220000Mmωω−Ω−, which leads directly to the above solution. 22. m m 2m k K k θ3θ2θ1We “scale” the force constants and masses to 1 unit, namely, 11mandk==. Let k1K andl′ ==such that 3l= circumference So: 222123122Tθ=++±±±222222113312332111111222222VK2Kθθ=−+−+−+−+−+−Collecting terms … () ()1
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.