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Triple pendulum
A triple pendulum has three strings of equal length a and the three particles (starting from the top) have masses 6m, 2m, m respectively. The pendulum performs small oscillations in a vertical plane. Show that the normal frequencies satisfy the equation
12µ3 - 60µ2 + 81µ - 27 = 0.
where µ = aω2/g. Find the normal frequencies, the forms of the normal modes, and a set of normal coordinates. [µ = 3 is a root of the equation.]
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