The speed of the bob of a simple pendulum is maximum at its ______.

Explanation

To solve the question, "The speed of the bob of a simple pendulum is maximum at its ______," we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Pendulum Motion**: A simple pendulum consists of a mass (the bob) attached to a string that swings back and forth under the influence of gravity. The motion can be analyzed in terms of potential energy and kinetic energy.

2. **Identifying Positions**: The pendulum has two extreme positions (maximum displacement from the mean position) and one mean position (the lowest point in the swing).
- Extreme positions are where the pendulum is at its highest points on either side.
- The mean position is the lowest point of the swing.

3. **Energy Considerations**:
- At the extreme positions, the pendulum has maximum potential energy and minimum kinetic energy. This is because the bob is momentarily at rest at these points.
- At the mean position, the pendulum has minimum potential energy and maximum kinetic energy. This is because the bob is moving the fastest at this point.

4. **Kinetic Energy and Speed**: Kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2}mv^2 \]
where \(m\) is the mass of the bob and \(v\) is its speed. Since kinetic energy is maximum at the mean position, it implies that the speed of the bob is also maximum at this position.

5. **Conclusion**: Therefore, the speed of the bob of a simple pendulum is maximum at its mean position.

### Final Answer:
The speed of the bob of a simple pendulum is maximum at its **mean position**.

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