In an oscillating pendulum the ............... energy is maximum at extremes.

Options

A. potential
B. vibrational
C. gravitational potential
D. kinetic

Explanation

To solve the question, "In an oscillating pendulum the ............... energy is maximum at extremes," we need to analyze the energy transformations that occur in a pendulum as it oscillates.

### Step-by-Step Solution:

1. **Understanding the Pendulum Motion**:
- A pendulum swings back and forth in a periodic motion. It has two extreme positions (the highest points of its swing) and a mean position (the lowest point).

**Hint**: Visualize the pendulum's motion and identify the extreme and mean positions.

2. **Energy Types in a Pendulum**:
- There are two main types of energy in a pendulum: kinetic energy (KE) and potential energy (PE).
- Kinetic energy is the energy of motion, while potential energy is the stored energy due to its height.

**Hint**: Recall the definitions of kinetic and potential energy.

3. **Energy at Extreme Positions**:
- At the extreme positions, the pendulum momentarily comes to rest before changing direction. This means that its velocity is zero at these points.
- Since kinetic energy is given by the formula \( KE = \frac{1}{2}mv^2 \), if the velocity \( v = 0 \), then the kinetic energy \( KE = 0 \).

**Hint**: Remember that kinetic energy depends on the speed of the pendulum.

4. **Energy Conservation**:
- The total mechanical energy of the pendulum remains constant throughout its motion. This total energy is the sum of kinetic and potential energy.
- If kinetic energy is zero at the extremes, then all the energy must be potential energy at that moment.

**Hint**: Think about the principle of conservation of energy.

5. **Conclusion**:
- Since kinetic energy is zero at the extremes, the potential energy must be at its maximum at these points.
- Therefore, the correct answer to fill in the blank is "potential energy."

### Final Answer:
In an oscillating pendulum, the **potential energy** is maximum at extremes.

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