N6722C: Roger that, Charlie. So, it is, indeed, a bug. I’ll go prowl around the “Bug Reports & Wishlist” neighborhood and see if any of the devs are aware of it and, hopefully, working toward a bit more realism. 
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Well, here is the most uneducated post you’re going to see i bet, but when my Cessna shakes. I disable the AP, click the AP Trim Button on left side of yoke, and re-enable AP. It is smooth sailing until i make an abrupt course change. I honestly havent researched why this works, but it works every time.
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This is a bug. There’s another post here: Default C172 G1000 Autopilot aileron oscillation problem (video included) - Bug Reports & Wishlist / Aircraft & Systems - Microsoft Flight Simulator Forums