For a particle undergoing SHM, the velocity is plotted aginst displacement. The curve will be

Options

A. a straight line
B. a parabola
C. a circle
D. an ellipse

Answer

To solve the problem of plotting the velocity against displacement for a particle undergoing Simple Harmonic Motion (SHM), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding SHM**:
- In SHM, a particle oscillates about a mean position. The displacement from the mean position can be positive or negative, depending on the direction of motion.

2. **Velocity and Displacement Relationship**:
- The velocity of a particle in SHM is maximum at the mean position (where displacement is zero) and decreases to zero at the extreme positions (maximum displacement).

3. **Graph Setup**:
- Set up a graph with the x-axis representing displacement (x) and the y-axis representing velocity (v).

4. **Analyzing the Motion**:
- As the particle moves from the mean position to the positive extreme, the displacement increases while the velocity decreases from its maximum value to zero.
- Conversely, as the particle moves back from the positive extreme to the mean position, the displacement decreases while the velocity increases from zero back to its maximum value.

5. **Negative Displacement**:
- The same pattern occurs when the particle moves to the negative extreme. The velocity again decreases to zero at the negative extreme and increases back to its maximum as it returns to the mean position.

6. **Shape of the Graph**:
- When plotting these points, the graph will show a continuous curve that resembles an ellipse. This is because the velocity decreases to zero at both extremes of displacement and reaches its maximum at the mean position.

7. **Conclusion**:
- Therefore, the curve representing the velocity against displacement for a particle undergoing SHM will be an ellipse.

### Final Answer:
The curve will be an ellipse.

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