which one of following is a simple harmonic motoin?

Options

A. Ball bouning between two rigid vertical walls
B. particle moving in a circle with unifrom speed
C. Wave moving through a string a string fixed at both ends
D. Earth spinnig about its own axis

Answer

To determine which of the following options represents simple harmonic motion (SHM), we need to analyze each option based on the definition of SHM. SHM is characterized by motion that can be described by a sine or cosine function.

**Step 1: Analyze the options.**

1. **Ball bouncing between two rigid vertical walls**:
- This motion is not periodic in the sense required for SHM. The motion cannot be represented by a single sine or cosine function.
- **Conclusion**: Not SHM.

2. **Particle moving in a circle with uniform speed**:
- Although the particle moves in a circular path, the projection of this motion onto one of the axes (x or y) can be represented as a sine or cosine function. For example, if we take the x-component as \( x = a \cos(\omega t) \) and the y-component as \( y = a \sin(\omega t) \), this satisfies the conditions for SHM.
- **Conclusion**: This is SHM.

3. **Wave moving through a string (fixed at both ends)**:
- While this represents a wave that can exhibit harmonic characteristics, it does not represent a single particle undergoing SHM. Instead, it describes the collective motion of many particles along the string.
- **Conclusion**: Not SHM.

4. **Earth spinning about its own axis**:
- This is a rotational motion and cannot be described by a sine or cosine function in the context of SHM.
- **Conclusion**: Not SHM.

**Final Conclusion**: The only option that represents simple harmonic motion is the **particle moving in a circle with uniform speed**.

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