Swept wings
172_driver,
I'm surprised no one has yet mentioned swept wings.
Straight wing aircraft do not suffer from dutch roll - unless you intentionally cause it by continually gently applying left and right rudder when you will get a yaw induced oscillatory rolling motion.
SOME swept wing aircraft exhibit dutch roll and the simple reason understandable to a mere Basil is as follows:
1. Aircraft yaws (eg to right).
2. Left wing sweep relative to airflow is reduced therefore:
a) Airspeed normal to leading edge is increased so V increases.
b) Camber to airflow is increased so CL increases. (remember L= CL*1/2*p*V2*S)
c) Lift on left wing increases so left wing rises (slightly assisted by sideways lift on fin).
3. Increased drag on left wing and fin lift opposing yaw now stop right yaw and aircraft yaws to left.
4. Aircraft overswings to left, right wing rises etc etc.
5. "Bu**er I!" says pilot putting down coffee and page 3 of 'The Sun' "Now what did they say to do when this happens?"
If the resulting phugoid is divergent it will continue until the aircraft departs controlled flight - unless, of course, the pilot corrects with a timely and controlled input of aileron.
Some swept wing jets, whose clever aerodynamicists and structural engineers got it just right (eg B747) do not dutch roll.