It is worth considering that the F28 is an aircraft that was designed and built in the 1960s. It doesn't have an autothrottle, and the autopilot is very rudimentary (often with only on/off modes).
I recall during testing that I did experience similar oscillations, but after discussing them with our flight model developer and F28 experts, we came to the conclusion that they were mostly always caused by me trying to fly the F28 like a modern airliner with a sophisticated autopilot. I'll post some tips below that have helped me fly the F28 more realistically:
Avoid making large, sudden changes to the vertical speed. With V/S mode enabled, the F28s autopilot will command whatever vertical speed is selected on the altitude preselect controller. If the V/S is instantly increased from 0 to 2000ft/min, the aircraft is going to pitch up at its maximum rate and will likely overshoot the vertical speed target and will take a few osciallatiosn to settle on it. It is good practice in any aircraft, especially older ones, to slowly increase/decrease the vertical speed for passenger comfort. For this, try increasing/decreasing the vertical speed knob in the range of 1-3 notches per second, and see if that improves the osciallations.
Ensure the selected V/S matches the aircraft's current V/S before enagaging V/S mode. For similar reasons as above, if the aircraft is in level flight and V/S mode is selected with the V/S knob already set to 2000ft/min, the aircraft is going to pitch up at its maximum rate and overshoot the vertical speed target. The best procedure for using V/S mode is to first set the V/S knob to match the aircraft's current vertical speed, then engage V/S mode, then slowly increase/decrease the V/S knob to the desired V/S speed.
Preempt altitude capture in a descent by increasing engine power. In a modern airliner, the autothrottle systems will most likely increase engine power as the aircraft levels off in a descent. This ensures the aircraft's airspeed remains the same throughout the altitude capture phase, and the aircraft will maintain similar momentum. As the F28 doesn't have an autothrottle, this power increase must be done manually. As the aircraft enters the altitude capture phase, you'll want to slowly increase engine power to maintain the same airspeed as you were at in the descent.
All three points above will come more naturally as you start to fly the aircraft more. Just like the real pilots, you'll start to understand the aircraft's quirks, and you'll find the techniques that work best for you.
See how you get on with the above tips.
If you do still experience oscillations on future flights, could I kindly ask you to raise a ticket with Just Flight Support at the following link: https://www.justflight.com/support
In the ticket, if you could provide specific examples of when the oscillations occur (i.e. provide steps for how our support team can reproduce the behaviour), and if possible, send us a video of the behaviour, then we will be in the best position to be able to assist with further troubleshooting, or we'll have enough information to pass onto our development team for further investigation.
Mark - Just Flight