Analytical Mech Homework Solutions 183

Analytical Mech Homework Solutions 183 - 20 a1 = 0 and a2 =...

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20 12 01 a and a == Thus, the normal modes are approximately … 00 10 it i t e and e ω    QQ Note 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 … 2 m 2 KM () 22 0 0 0 0 M m ωω Ω− , which leads directly to the above solution. 22. m m 2m k K k θ 3 θ 2 θ 1 We “scale” the force constants and masses to 1 unit, namely, 11 m and k = = . Let k 1 K and l ′ = = such that 3l = circumference So: 222 123 1 2 2 T θ =+ + ±±± 2222 2 21 13 31 23 32 11111 1 22222 2 VK 2 K θθ =−+−+−+−+ −+ Collecting terms … () () 1
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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.

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