The motion of a simple pendulum is

Options

A. exactly simple harmonic
B. exactly rectilinear
C. approximately simple harmonic
D. none of these

Explanation

To determine the nature of the motion of a simple pendulum, we can analyze its characteristics step by step.

### Step-by-Step Solution

1. **Understanding Simple Harmonic Motion (SHM)**:
- Simple Harmonic Motion is defined as a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction.
- The motion of a simple pendulum can be compared to SHM when the angle of displacement is small.

2. **Analyzing the Motion of a Simple Pendulum**:
- A simple pendulum consists of a mass (bob) attached to a string or rod that swings back and forth under the influence of gravity.
- When the pendulum is displaced from its equilibrium position and released, it swings to the opposite side and returns to the starting point.

3. **Conditions for SHM**:
- For the motion to be classified as SHM, the angle of displacement must be small (typically less than 15 degrees). In this case, the motion can be approximated as SHM.
- As the angle increases, the motion deviates from SHM due to the non-linear nature of the restoring force.

4. **Energy Losses**:
- In real-life scenarios, a simple pendulum experiences energy losses due to air resistance and friction at the pivot point.
- These losses result in a gradual decrease in the amplitude of the swing, causing the pendulum to eventually come to rest.

5. **Conclusion**:
- Given that the motion of a simple pendulum can be approximated as SHM for small angles but is affected by energy losses, we conclude that the motion of a simple pendulum is **approximately simple harmonic motion**.

### Final Answer:
The motion of a simple pendulum is approximately simple harmonic motion.

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