1211.17 k k 2m m x2x1 Note: As discussed in Section 3.2, the effect of any constant external force on a harmonic oscillator is to shift the equilibrium position. x1and x2are the positions of the harmonic oscillator masses away from their respective “shifted” equilibrium positions. ()2212112Tmxmx=+±±22Vkx kxx=+ −1LTV=−2,dLLmxkxk xxdtxx∂∂==−+±1−220mxkxkx+−=2,Lmxk xxdtxx−±1−221mxkxkxThe secular equation (11.4.12) is thus 22202mkkkmkω−+−=−−+2422225 2mmkkkωω+0=The eigenfrequencies are thus … 25174km±=The homogeneous equations (Equations 11.4.10) for the two components of the jtheigenvector are … 2122202jjakak−=+For the first eigenvector (the anti-symmetric mode, j = 1) …
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