Does Frequency Affect Amplitude?

A small particle having charge \(q\) is at rest between the two plates. When an alternating voltage source \(V = V_0 \sin ( \omega t )\) is connected across the plates, it is observed that the particle oscillates with amplitude \(A\).

If the frequency of the voltage source is doubled, \(V' = V_0 \sin (2 \omega t)\), then what would be the new amplitude of the particle?

Note: Ignore gravity.

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