Differential Equations Quiz
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SYSTEMS OF DIFFERENTIAL EQUATIONS
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Consider a three-mass system where only masses 1 and 2 are coupled directly, but all three masses are connected to ground springs. If the coupling between masses 1 and 2 is removed, the individual frequencies are ω1=2\omega_1 = \sqrt{2}, ω2=3\omega_2 = \sqrt{3}, and ω3=5\omega_3 = \sqrt{5} rad/s. When weak coupling with strength ϵ\epsilon is restored between masses 1 and 2, what is the first-order perturbation correction to the frequency of the middle mode?
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