2431310yyxx−−−=We introduce three generalized coordinates Q, q1and q2that should be close to what we guess would be normal modes … 13113 2 13;;Qx x q xx q y y=+=−Solve for xi, yiin terms of Q, q1and q2using the above 3 equations of constraint … ()112133;22m1xQqxQx x xM=−=−12223myqQyqyQqM=−2Thus, the kinetic energy, in terms of these generalized coordinates, is … 11244mTmQ mq mqMMµ=+ ++±±±2where 2Mmis the mass of the H2S molecule The potential energy is … 22221112884mVkQkq kq kqµµ++−12qMNote, that in the Lagrangian , the only cross term is one involving qq. therefore, Qis a normal mode with eigenfrequency given by the ratio … LTV21QQQkmKMmMω==+Constructing the residual 2x2 Kand Mmatrices involving only q1and q2terms, which we will call Kqand Mqgives … 042Mand0M−
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