My washing machine on a pedestal shakes the whole floor. What can I do to reduce the vibration?

Your machine's leveling feet are the first place to look. An unbalanced load or unlevel machine on a pedestal will always cause excessive vibration. After checking the leveling feet and ensuring your load isn't tangled, if it still shakes, your wood floor likely isn't stiff enough for the machine's high-speed spin cycle. Anti-vibration pads offer minimal improvement for a truly weak floor. Reinforcing the floor joists or adding blocking is the proper solution, but that's a structural job for a carpenter or engineer and might need a permit.