How can I prove peroidic of state of simple harmonic

Thread starter Asal
Start date Sep 14, 2009
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Harmonic State

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To prove the periodicity of the state of simple harmonic motion, one can start by analyzing the function Y(x) given in the discussion. The periodic nature can often be established by demonstrating that Y(x + T) = Y(x) for some period T. The approach involves examining the terms in the expression, particularly the exponential components, to identify their periodic characteristics. Utilizing the relationship f(x + t) = f(x) can help in this analysis, although the specific application may require careful manipulation of the terms. Understanding the underlying mathematical properties of the components is crucial for proving periodicity.

Sep 14, 2009

Asal

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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Sep 14, 2009

berkeman

Admin

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?

Sep 16, 2009

Asal

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

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