 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-2/17/f/solution

The largest angular-frequency magnitude is

ω_{3} = (2 + 2) k / m

. With overall amplitude

A

, the corresponding displacements are

x_{1} = x_{3} = \frac{A}{2} cos (ω_{3} t), x_{2} = - \frac{A}{2} cos (ω_{3} t) .

Thus the two outer masses move together, while the middle mass moves oppositely with

2

times their amplitude. All three have the same period

2 π / ω_{3}

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