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Consider a heavy particle of mass m is place at the top (on the outside side, not inside) of a vertical hoop of radius R and mass M. The hoop can slide on the ground without any friction along the x-axis. Calculate the reaction of the hoop on the particle by means of the Lagnrang'e undetermined multipliers:

a. write the lagrangian

b. derive lagrange's equations

c. find the location of the hoop center X as a function of angle theta of the falling particle.

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