5. (20pts) Two pendulums of equal length I are coupled with a spring of spring constant k between the bobs. The masses o

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5 20pts Two Pendulums Of Equal Length I Are Coupled With A Spring Of Spring Constant K Between The Bobs The Masses O 1 (31.74 KiB) Viewed 20 times

5. (20pts) Two pendulums of equal length I are coupled with a spring of spring constant k between the bobs. The masses of the bobs are identical and the generalized coordinates for the pendulum positions are 0 and 0. Given the following secular equation and angular frequencies for this system: a) Find the two normalized eigenvectors for the system. b) Find expressions for the 2 normal modes, 11 and 12, in terms of the 6 and 0 coordinates. {A – mw?} = {mgl + kl2 ,z mw?12 -kl? mgl + kl2 - ma mw=12} - W1 W2 = 22K m