What would hapen if an object virated at the frequency of light?

The speed of light is a speed, not a frequency.  People don't usually talk about the frequency of light -- instead, they give you the color, or the wavelength.

As for the frequency of light, if we're talking visible light, then the frequency is around 4x10^14 hertz.   It's pretty much absurd for a macroscopic object to vibrate at that frequency (at least not in a way we could measure), but if it did, the amplitude would have to be very very very tiny, and so nothing would happen.

Radio waves are the same as light, but they have lower frequencies.  An object vibrating at 60 KHz (the frequency of the radio wave used by your `Radio controlled (or Atomic, but it's not atomic) clock' is certainly possible and measurable.

It's not impossible.  It happens all the time.

An electron is shaken up and down an antenna at radio frequencies and thereby emits fadio waves.  Something somewhat (although you need quantum mechanics to understand it) similar happens in an atom when an electron shifts energy levels and emits a photon of light frequencies.