surely you can visualize the motion of a damped pendulum.
It starts with maximum displacement and zero velocity, it heads towards the origin with increasing velocity, passes the origin with maximum velocity, and heads towards maximum displacement of the opposite sign with decreasing velocity finishing at maximum displacement and zero velocity.
It then reverses direction and goes through the same sequence of steps.
Over time as they note the maximum displacement decreases to 0.
With position on one axis and velocity on the other what well known curve does this make?