If the amplitude of a simple harmonic oscillator is doubled, by what multiplicative factor does the angular frequency change?

No change

Explanation:

In a simple harmonic motion, we have that

y = A sin(wt), where

w is the said angular frequency

The angular frequency w, is given as √(k/m)

If the amplitude, A is doubled it will have no corresponding effect on the angular frequency, w, because they do not depend on each other. A is independent of w, and w is independent of A. And as such, no matter the change in either, it doesn't affect the other

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