Randy Zimmerman wrote:

I use an old knife blade clamped in the jaws of a vise. I then
balance
the blade with the knife edge running across the center of the hole.
Grind the edges to balance. You will never get the blade to sit
stationary but you will see which end is heavy. If the mower is
shaking enough to feel in your shoulders I suspect that the motor
shaft is bent.

It might be worth removing the blade and running the motor to see if it still shaking or the shaft is visibly
wobbling. If it is, then a new or balanced blade is a waste of money and/or time.