In an experiment , to find the loss of energy with respect to time in case of swinging simple pendulum , the graph between `(amplitude)^2` and time is

Options

A.
B.
C.
D.

Answer

To solve the problem of finding the graph that represents the relationship between the square of the amplitude and time for a swinging simple pendulum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Pendulum Motion**: A simple pendulum swings back and forth, and as it does so, it gradually loses energy due to air resistance and friction. This loss of energy leads to a decrease in the amplitude of the pendulum's swing over time.

2. **Identify the Relationship**: As the pendulum loses energy, the amplitude (A) of the swing decreases. Since we are interested in the square of the amplitude (A²), we can say that A² will also decrease as time increases.

3. **Graphical Representation**: We need to find a graph that shows a decrease in A² with respect to time. This means that as time increases, A² should decrease.

4. **Analyze the Options**:
- **Graph A**: This graph shows a hyperbolic curve that decreases as time increases. This indicates that A² is decreasing, which is consistent with our understanding of a pendulum losing energy.
- **Graph B**: This graph shows a straight line that increases with time, which is incorrect as it suggests that A² is increasing.
- **Graph C**: Similar to Graph B, this graph shows A² increasing with time, which is also incorrect.
- **Graph D**: This graph shows A² decreasing initially and then increasing, which does not represent the behavior of a pendulum losing energy.

5. **Conclusion**: The only graph that correctly represents the relationship between the square of the amplitude and time, considering the loss of energy in a swinging simple pendulum, is **Graph A**.

### Final Answer:
The correct graph between (amplitude)² and time is **Graph A**.

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