What is the relationship between Q factor and spectral emmision line width?

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I have no ideal where to begin on this question.

Light of wavelength 0.6x10^-6 meters is emmited by an electron in an atom behaving as a lightly damped SHM with a Q factor of 5x10^7. Determine the width of the spectral emmision line.

I am thinking E=hv=A^2

where A^2=Q^2 for large Q.

but, in all realality, I am just pulling these relationships from the text. I don't intuitivly understand why Amplitute and the Q value would roughly be the same, nor do I understand why Energy would equal just A^2, as opposed to A^2cos^2(wt).
 
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