(a) Two identical masses m are constrained to move on a horizontal hoop. Two identical springs with spring constant k connect the masses and wrap around the hoop (see Fig.). Find the normal modes. 

(b) Three identical masses are constrained to move on a hoop. Three identical springs connect the masses and wrap around the hoop (see Fig.). Find the normal modes.

(c) Now do the general case with N identical masses and N identical springs.

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