How can I prove peroidic of state of simple harmonic

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The discussion focuses on proving the periodicity of the state of a simple harmonic function represented by the equation Y(x)=exp(iwt/2 sum(Cn Un (x) exp(-iwnt)). Participants emphasize the importance of using the periodicity condition f(x+t)=f(x) to establish the periodic nature of the function. The conversation highlights the need for a clear understanding of complex exponentials and their properties in relation to harmonic functions.

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This discussion is beneficial for physics students, mathematicians, and anyone studying wave mechanics or harmonic analysis, particularly those interested in the mathematical proofs of periodic functions.

Asal
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Hi
How can I prove peroidic of state of simple harmonic

Y(x)=exp(iwt/2 sum(Cn Un (x) exp(-iwnt) )
 
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Asal said:
Hi
How can I prove peroidic of state of simple harmonic

Y(x)=exp(iwt/2 sum(Cn Un (x) exp(-iwnt) )

Welcome to the PF. How would you usually approach proving that a function was periodic?
 


I usually use f(x+t)=f(x), but here I am not sure how can I prove it.
 

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