Shaking at take-offs and stopped at nuetral
 

Good morning ladies and gents, wondering if you all can help me figure why my 02 Sonata V6 shakes vibrates in acceleration for a sec or two, and it also vibrates/shakes (not much) in nuetral. As soon as the car rev's for a few sec's it goes away. It's just annoying. Dont wanna sell the car that way. I have done tune-up, oil-change, timing belt replaced, and all the fluids topped off. A couple of months ago I took the car to dealership in El Paso to replace timing belt. Recieved car back but would make humming noise only with ac on. Car felt good until three weeks ago. I started to hear a pinging noise under hood, the car had no oil. Drain plug was tight and no sign of an oil leak. Well I think dealership forgot to replace some of the oil lost or decided to drain it and not fill it. This urk'd the hell out of me. Had to replace it with new oil and a STP treatment and later that evening the noise went away. But that is when the shaking/vibration started at take offs or stopped in nuetral.

Can anyone give me some insight or clues on where to begin to diagnose the problem.

Marco