**Periodic Motion**

Periodic motion refers to the motion that repeats itself at regular intervals of time. It is characterized by the object or body oscillating or moving back and forth over the same path. The motion of a pendulum is a classic example of periodic motion.

**Explanation**

Let us analyze each option and determine which one exhibits periodic motion:

a) Train: The motion of a train is not periodic. Trains move in a straight line or along a curved track, but they do not repeat the same motion over and over again.

b) Pendulum: The motion of a pendulum is periodic. A pendulum consists of a mass (bob) attached to a fixed point by a string or rod. When the pendulum is displaced from its equilibrium position and released, it swings back and forth in a regular manner. The time it takes for the pendulum to complete one full swing (from one extreme to the other and back) is called the period. The pendulum will continue to swing back and forth with the same period as long as there is no external force or friction acting upon it.

c) Aeroplane: The motion of an airplane is not periodic. An airplane moves in various directions depending on the pilot's control inputs and the external forces acting upon it. It does not repeat the exact same motion over and over again.

d) Flying bird: The motion of a flying bird is not periodic. Birds can fly in various patterns and directions, and their motion is not repetitive.

**Conclusion**

Based on the analysis, the only object that exhibits periodic motion is a pendulum (option B). The motion of a pendulum is characterized by its regular back and forth swinging motion, which repeats itself at regular intervals of time.

B is the answer.