Why at times does my car sound like I hit something when I change my gear?

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There has been a couple occasions where my car will make a screeching noise and sounds like I hit something when changing my gear from reverse to drive. I experimented last time it happened; when changing the gear (didn't drive my car) from park to drive it made a noise that sounded like my car was dropping (big thud) and when i put it in park it would shoot forward and then bounce back. I noticed where my car normally says the gear that it is in wasn't on both time this has happened.0, but when I op turn my car off and back on it works again as if nothing is wrong.