An air filled parallel plate capacitor, with plate area $$A$$ and plate separation $$d$$, is connected to a battery of emf $$V$$ volt having negligible internal resistance. One of the plates of the capacitor vibrates with amplitude $$a$$, where $$a\ll d$$, and angular frequency $$\omega$$. If the instantaneous current in the circuit reaches a maximum value $$I_0$$, the amplitude of the vibrations is $$a$$ equal to