there can be number of issues,
1- Wheel balancing issue, Rims cud be bent, rubber might have deformed.
2- also get the alignment checked, shop will let u know if any suspension part is weak, mostly the control arm big bush gets damaged.
3- the Auto has this issue of vibration due to inner axles, do get them checked if they have some play in them, if so then it will vibrate a bit when u r trying to accelerate the car.
4- Do verify the engine mounts,
