This is a basic question about energy conservation and classical mechanics:
Question: Under what situations can this motion be perpetual?
Without gravity and without frictions.
Without gravity and with frictions.
With gravity and without frictions.
With gravity and with frictions.
Others setup (please state the setup)
Impossible to be perpetual
Gravity (say) is along the vertical $y$ direction, with a constant gravitational force and a linear gravitational potential $V(y)=mgy$.