If two bodies are coupled and they are performing oscillations, then do they have only two allowed frequencies (normal modes frequencies) with which they can oscillate or do they have a number of frequencies that depends upon their normal modes frequencies?
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$\begingroup$ Review your system which has two degrees of freedom, hence two normal modes. In this two dimensional space, you have an infinity of solutions, relying on these two natural frequencies. What is the question? $\endgroup$– Cosmas ZachosCommented Jan 29 at 14:30
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$\begingroup$ Linked, and also. $\endgroup$– Cosmas ZachosCommented Jan 29 at 14:34
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$\begingroup$ I was confused thought that particles will have only two frequencies for oscillations, thanks for the clarification. Do those infinite solutions depend upon these two natural frequencies linearly? $\endgroup$– Nikhilesh SinghCommented Jan 29 at 15:05
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$\begingroup$ They are linear combinations of the two natural frequency solutions, so, then, amount to trigonometric functions of the sum and difference of solutions. Have you read up on beats in the first link? $\endgroup$– Cosmas ZachosCommented Jan 29 at 15:09
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$\begingroup$ No not yet but I will read that paper for sure. Thanks for your time. $\endgroup$– Nikhilesh SinghCommented Jan 29 at 15:15
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