It's all been said. My JD X750 is electric engagement. Pull the knob and off she goes. Sometimes it will vibrate, a little, at initial engagement but it smoothes right out at operating speed.
In addition to this list: " Inspect blades, pulleys, idlers and belts. Something is either bent, worn or out of alignment.", also inspect the spindles and their bearings. Yours is doing the opposite of what is normal, getting worse with RPMs.
Agree with all points made. However, I lean toward worn/damaged parts. Typically an out of balance blade while never stopping to shake, reduces with greater rpms.
With your vibration worsen with higher rpms, I really expect a bearing with sufficient wear that the shaft is moving when spinning. Although it well could be a bent shaft as well.
This is another thread where we don't have enough information. How old is this deck? How long has the OP had it? Has any kind of ground object been hit? Did this come on suddenly or gradually?