Analytical Mech Homework Solutions 175

# Analytical Mech Homework Solutions 175 - 12 11.17 k m x1 k...

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12 11.17 k k 2m m x 2 x 1 Note: As discussed in Section 3.2, the effect of any constant external force on a harmonic oscillator is to shift the equilibrium position. x 1 and x 2 are the positions of the harmonic oscillator masses away from their respective “shifted” equilibrium positions. () 22 12 11 2 Tm x m x =+ ±± 2 2 Vk x k xx =+ − 1 LTV =− 2 , dL L mx kx k x x dt x x ∂∂ == + ± 1 2 20 mx kx kx +−= 2, L mx k x x dt x x ± 1 221 mx kx kx The secular equation (11.4.12) is thus 2 2 2 0 2 mk k km k ω −+ = −− + 24 2 2 2 25 2 mm kk k ωω + 0 = The eigenfrequencies are thus … 2 51 7 4 k m ±  =   The homogeneous equations (Equations 11.4.10) for the two components of the j th eigenvector are … 2 1 2 2 2 0 2 j j a k a k = + For the first eigenvector (the anti-symmetric mode, j = 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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