Simple harmonic motion angular frequency

There are many different solutions for X1 and X2 to this pair of coupled equations, but it proves possible to find two particularly simple ones called normal modes of vibration. These have the property that both particles execute simple harmonic motion at the same angular frequency. Not only that, every possible vibrational motion of the two particles can be described in terms of the normal modes, so they are obviously very important. 

Under the conditions of the experimental method, the sample will exhibit simple harmonic motion, and thus the angular frequency (co) may be related to the shear modulus (G) ... 

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