This cyclic ozone(O3) where bonds can be described by springs with strength 𝑘, and 𝑀 is the atomic mass

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This cyclic ozone(O3) where bonds can be described by
springs with strength 𝑘, and 𝑀 is the atomic mass of Oxygen.

This Cyclic Ozone O3 Where Bonds Can Be Described By Springs With Strength K And M Is The Atomic Mass Of Oxygen 1 Fi 1 (10.81 KiB) Viewed 45 times

1) Find the classical Lagrangian for this system, using the
positions of each atom {𝑥i} and the velocities of each
atom {𝑥̇i} as generalized coordinates. Assume the
vibrations can only occur along the axis of the molecule.
2) Use the Euler-Lagrange equations to find the normal
modes of the system(assuming a simple harmonic solution).
Have only real, positive frequencies.
3) Find the Hamiltonian of this system in terms of the atomic
momenta and the atomic positions.