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Coupled Oscillators-eigenfrequencies and normal modes

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Consider a system like the system in fig 2 except there are 3 equal masses M, and 4 springs all with equal spring constants K. with the system fixed at the ends.

Find the eigenfrequencies and describe the normal modes for this system

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Solution is provided in a 2-page word document. Solution to this graduate level question is provided using coefficient matrix technique. A wonderful question and answer pair for your collection.