Non rigourous observations from a non test pilot with a couple of years on 3/4/5s: I would say that:
- during automatic flight.
- the b737-500.
- is not optimally damped in pitch.
i.e. it takes a lot more than one oscillation to damp out pitch disturbances. This seems most apparent during climb and descent with pitch mode controlling speed. Long time period oscillations of +/- 10 kts seem to be typical. However I have also seen +/- 700 fpm in Alt Hold or VNAV PATH during level flight.
I am told that the aircraft uses the same control law as the -400, though I stress I have no idea if that is true or not.
On a similar vein, having the ap and fd disagreeing in pitch for quite long periods during climb and descent seems to be a 'feature of the model'.
CPB