When the amplitude of vibrations of a simple pendulum is increased, then its time-period :

Options

A. decreases
B. increases
C. remains the same
D. first increases and then decreases

Answer

To solve the question regarding the effect of increasing the amplitude of vibrations of a simple pendulum on its time period, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Pendulum**:
- A simple pendulum consists of a mass (bob) attached to a string that swings back and forth around a mean position. The distance from the mean position to the extreme position is called the amplitude.

2. **Defining Time Period**:
- The time period (T) of a pendulum is the time taken to complete one full cycle of motion, which includes moving from the mean position to one extreme, back to the mean position, and then to the other extreme, before returning to the mean position.

3. **Effect of Amplitude on Time Period**:
- The time period of a simple pendulum is primarily determined by its length (L) and the acceleration due to gravity (g). The formula for the time period of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- From this formula, we can see that the time period (T) does not depend on the amplitude of the pendulum.

4. **Conclusion**:
- Therefore, even if the amplitude of the pendulum's vibrations is increased, the time period remains unchanged. This means that the correct answer to the question is that the time period remains the same.

### Final Answer:
The time period of a simple pendulum remains the same when the amplitude of vibrations is increased.

---