But I didn’t!
I have a 05 Grand Am SE that I bought used.
When I coast (have noticed it at 35 - 45mph but that doesn’t mean it isn’t happening other times) it feels as though something under the car is pulling back once every second or so. Almost as though I’ve tapped the brakes very lightly (but I haven’t). I don’t know why I say it feels like it’s under the car, except that’s what it feels like. Sometimes it even feels like a two-part hesitation (front,back,one second fine,front,back…) but that REALLY may be my imagination.
It’s enough to make me sway slightly forward so it’s not ALL in my head.
When I bought the car, Carfax showed it was a rental and didn’t list any accidents or other negatives - but since then I have found that it at least had an accident that knocked the right headlight can so the light pointed about 45 degrees above the horizon. Don’t know if that’s helpful information.
Just had my brakes done - front, back and rotors. The whole brakechilada. Just trying to supply you with anything that might help figure it out!
Torque converter clutch locking and unlocking, maybe?
About 35 - 45 mph is the speed the torque converter locks (acceleration) and unlocks (deceleration). There may be a TCC (Torque Converter) fuse you can pull to find out if it is the torque converter lock. A transmission shop is the place to go.
Since there isn’t a check engine light coming on, I won’t guess at an engine misfire causing this.
Hi, original poster here…
What would happen when I pulled the Torque Converter fuse if it was the problem? What would happen if it wasn’t?
I really appreciate the help - between having to buy new brakes 6 months after purchasing the car, the headlight/unreported accident and now this, I’m thinking this may be my first and last ever used car purchase 
If you disable the torque converter lockup, by pulling the fuse, the problem should cease. If not, the fault is elsewhere. The TCC fuse, or relay, may be in a fuse/relay box under the hood. This is NOT a cure. It’s just to determine where the problem lies. Once that is found, further diagnostics/repair can be donee
A lot of fuel injection systems will cut fuel while coasting with the throttle valve closed. If you have your foot lightly on the gas pedal, the system may go in and out of fuel cut giving you the forward/backward jostle. As stated previously, the torque converter will unlock at closed throttle on some cars. If the throttle position sensor has an ambiguous position, it is possible the TC is unlocking and relocking causing the jostle.
This also could be a drivability problem so you might run the car by a powerplant technician for diagnosis. Also, you might see if you can drive another 05 Grand Am to see if it also has the jostle.