Coupled Forced Oscillators- Small Question-

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SUMMARY

The discussion focuses on the dynamics of a triatomic molecule consisting of two masses (m) at the ends and one mass (2m) in the center, connected by springs with spring constant k. The highest frequency mode is identified as ω² = 2k/m, occurring when the end masses oscillate in phase while the middle mass oscillates in counterphase. The question posed is which mass should be excited to achieve optimal resonance with the highest frequency mode. It is concluded that exciting the middle mass may require less energy for resonance.

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I have the infamous triatomic molecule, with two m masses in the extremes and one 2m mass in the middle, joined by two k springs. I have worked all through the problem (found frequencies, normal modes, drawn configurations, initial conditions) with no hindrances, but I can't seem to get the last question.

It says: If a harmonic force is applied to one of the masses, to which would it be better to excite better the highest frequency mode?

Btw, the highest freq. mode is w^2= 2k/m and it happens with the first and third masses are in phase, with the middle mass in counterphase (1,-1,1)

How do I know which mass should I excite?

Thanks

Sol.[/color]
 
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You can try both, and then see which one gives better resonance. My intuition tells me that the mass in the middle would be the one. I'm assuming that "better" means "less energy required."
 
Thanks

Sol.[/color]
 

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