So recently I have been studying A.C. circuits and the graphs show that the current oscillates itself as a function of time. Now, according to me an oscillating body vibrates. Hence, the oscillating electric current should also make the medium oscillate in which it is flowing. Am I correct in my assumption, if not then why?
Oscillating does not always mean vibrating. Oscillation simply means some measurable value is cycling back and forth. This could be a vibration, which would be a measurable change in position, back and forth (like a grandfather clock or your phone's vibrator), but oscillation is a more general concept. For example, in linguistics, we talk of oscillation in linguistic patterns which seem to go back and forth, back and forth. There's no physical movement in that case, but there's still an oscillation.
AC does not automatically mean vibrating. It's merely the fact that the measurable current is oscillating between forwards and backwards. Technically, electrons are moving, but you'll find its a very tiny effect.
However, you will find things operating on AC do in fact vibrate. This is due to second order effects. The changing current can cause changing magnetic fields, which can draw components together and push them apart in tune with the AC oscillations. This is the source of the humming you will hear from many devices.
Some components such as resistors, most (but not all) capacitors, and semiconductors aren't very prone to vibration. Other components like transformers are and have to be constructed to prevent audible vibrations. Back when CRTs were very common, it was not unusual for the coil(s) in their flyback transformer to loosen over time and cause a high-pitched noise. It could be downright annoying for those who could hear it.
today i was using my computer and noticed one of my post-it notes on my monitor vibrating a little. It was resting slightly on the power cord to the keyboard. I thought well isn't that odd and as i moved the keyboard the vibration stopped. I thought hmm AC current is oscillating so could it be causing a minute vibration detected by the post-it note, so i moved the cord back to where it was just barely touching and viola it started vibrating again. Just my 2 cents.