A pendulum

A pendulum is a simple mechanical device that consists of a weight (also known as a bob) attached to a rod or string. It is commonly found in wall clocks and performs oscillatory motion, swinging back and forth.

Oscillatory Motion

Oscillatory motion refers to the repetitive back and forth motion of an object around a central equilibrium position. In the case of a pendulum, the bob swings from one side to another in a regular pattern.

Time Period

The time period of a pendulum is the time it takes for one complete oscillation, or one swing from one side to the other and back. The time period of a pendulum is determined by its length and the acceleration due to gravity. It is independent of the mass of the bob.

Fixed Time Period

The time period of a pendulum is fixed because it depends only on the length of the pendulum and the acceleration due to gravity. For a given pendulum, if the length remains constant, the time period will also remain constant. This is why pendulum clocks are known for their accuracy in keeping time.

Explanation of Options

- Option a) a pendulum: This is the correct answer because a pendulum, with its oscillatory motion and fixed time period, fits the description provided in the question.

- Option b) bob of a pendulum: While the bob is an essential part of a pendulum, it alone does not perform oscillatory motion. It is the entire pendulum system that swings back and forth.

- Option c) pendulum clock: While a pendulum is a key component of a pendulum clock, the question specifically asks about a part of a wall clock. A pendulum clock is a specific type of clock that uses a pendulum as its timekeeping element.

- Option d) None of these: This option is incorrect as the correct answer is option a) a pendulum.

Conclusion

In conclusion, the part of a wall clock that performs oscillatory motion with a fixed time period is a pendulum. It swings back and forth in a regular pattern, providing the mechanism for accurate timekeeping.