01 vibration during normal speeds

My 01 Century just had new tires(balanced) put on 3 weeks ago. I noticed a vibration in it now 2 weeks ago gradually getting worse. More so at 30 mph with gradually speeding up to 60. I took it back to where the tires were done and they rechecked the balance and made sure there wasnt any broken or slipped belts, they said all was okay with the tires. There is no vibration in the steering wheel at any speed. Anyone have any ideas what this could be caused from? Thanks.

does the vibration change when the brakes are applied (lessens or gets worse?), is it worse while accelerating or at steady speed?

Its worse while speeding up. Dont notice anything when applying brake.

If not in the steering where do you feel it, I assume they rechecked the rear tires also?

They rechceked all 4 tires. It feels like the front is shaking to the right and the rear is shaking to the left, then visa versa, dont know how else to explain it. While speeding up I can actually see my legs shake back and forth a little from what the cars doing. Could it be my rear shocks?

does it shake only on accelleration or even when cruising at 60?

possible engine mount.

Are the tires a quality brand tire; as I have had cheap new tires balance ok but they had excess radial tire variation. As the tires are now 3 weeks old, the tire plies have relaxed, you could now have them road forced balanced to confirm. Typically this condition would worsen with road speed.

It only shakes during acceleration, if cruise is set at 60 it doesnt shake a bit, but if you try to accelerate to 65 then it shimmys until cruise at steady speed again. Tires are a Goodyear 75000 mile.

If this is not a misfire symptom I would look at front axle shafts and all the engine /trans mounts. From here it is tough to diagnose this type of problem.

sounds like misfire as maxwedge has posted.

you could try loading the engine with the car stopped. with the engine running in drive, the car stationary. e brake on and nothing closeby to run into. apply service brakes and hold then load engine by gently applying accellerator briefly (5sec). this creates a load on the engine which increases spark demand.