A triple pendulum has three strings of equal length a and

Question

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.]