which of the following is simple harmonic motion?

Options

A. Particle moving in a circle with uniform speed
B. Wave moving through a string fixed at both ends
C. Earth spinning about its axis
D. Ball bouncing between two rigid vertical walls

Answer

To determine which of the given options represents simple harmonic motion (SHM), we can analyze each option based on the characteristics of SHM.

### Step-by-Step Solution:

1. **Understand the Definition of 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.

2. **Analyze Each Option**:
- **Option 1: Particle moving in a circle with uniform speed**:
- This motion is not SHM because, although the speed is constant, the direction of the velocity changes continuously, resulting in centripetal acceleration. The acceleration is not directed towards the center in a linear manner as required for SHM.

- **Option 2: Wave moving through a string fixed at both ends**:
- This is indeed SHM because the particles of the string oscillate about their equilibrium positions, and the restoring force is proportional to the displacement from the equilibrium position.

- **Option 3: Heart spinning**:
- This motion does not qualify as SHM because it involves rotational motion rather than oscillatory motion about an equilibrium position.

- **Option 4: Ball bouncing between two rigid walls**:
- While this may seem periodic, it is not SHM because the motion does not involve a restoring force that is proportional to the displacement from an equilibrium position; rather, it involves elastic collisions.

3. **Conclusion**:
Based on the analysis, the only option that represents simple harmonic motion is **Option 2: Wave moving through a string fixed at both ends**.

### Final Answer:
The correct option that represents simple harmonic motion is **Option 2: Wave moving through a string fixed at both ends**.