More than likely it's either a motor mount or transmission mount.
Check your power steering fliud, if it is low this could cause the vibration you are feeling.
No it does not, you can have it installed or specially ordered like that.
When a 1993 Oldsmobile Cutlass makes a loud, moaning noise in reverse it is possible that the reverse gear in the transmission is getting ready to go out. The braking system should be looked at too, because of the vibration.
inspect the upper motor mount
drive shaft could be out of balance or tires could be out of round
Reverse is the term used in shows.
You might have a broken motor mount or broken transmission mount. the motor mounts were replaced one year ago.
Rebuild the transmission
Reversing polarity ,changes the rotation of the device you are changing polarity on.
I'm guessing it's an older car (as in at least 5 or more years, or a lot of miles). over time, the brackets that hold the motor to the chassis begin to wear, and the engine vibration becomes more apparent inside the car. this is made worse when you put more of a load on the engine by requiring it to power the headlights or engage the transmission.
Start by disconnecting the negative battery cable at the battery. Remove the radiator. Remove the drive belts and crankshaft pulley. Remove the Vibration Damper (Harmonic Balancer) bolt. Use a puller and remove the Vibration Damper. Reverse these instructions to reassemble. (Tighten the Vibration Damper bolt to the correct torque)
The engine may vibrate causing the front bumper pab=nel to rattle.