In the real world, periodic motion can be observed in the swing of a pendulum or the rotation of the Earth around the Sun. These motions are predictable and follow a set pattern, making them ideal for timekeeping and scientific study. On the other hand, non-periodic motion is evident in the movement of particles in the air or the swaying of tree branches. These motions are influenced by external factors and do not follow a predictable pattern, making them more challenging to study and predict.