On certain models the drivers seat bushings can wear out and the seat can rock back and forth. Replacing the bushings are needed to repair this issue.Google+
Car Problem Reports
Honda Civic Drivers Seat Bushings Can Wear Out
Honda Civic Problem
Average Mileage: 127,000 mi (36,000 mi - 203,000 mi)
It starts as a gentle little rock when you accelerate (speeding up or stopping).
Visitor, 2004 Honda Civic, 115,000 mi
Driver's seat rocks back and forth, and has since it was new.
drivers seat rocks back and forth