In `SHM` there is always a constant ratio between displacement of the body and its

Options

A. velocity
B. acceleration
C. mass
D. time period

Explanation

To solve the question regarding the constant ratio in Simple Harmonic Motion (SHM), we will analyze the relationship between displacement and the given options: velocity, acceleration, mass, and time period.

### Step-by-Step Solution:

1. **Understanding SHM**:
Simple Harmonic Motion is characterized by a restoring force that is proportional to the displacement from the equilibrium position. The equations governing SHM are important to understand the relationships between different physical quantities.

2. **Analyzing Velocity**:
The velocity \( v \) of a particle in SHM is given by the equation:
\[ v = \omega \sqrt{A^2 - x^2} \]
where \( \omega \) is the angular frequency, \( A \) is the amplitude, and \( x \) is the displacement.
- If we try to find the ratio of displacement to velocity \( \frac{x}{v} \), we can see that this ratio is not constant because it depends on \( x \) (the displacement) and changes as the particle moves.

3. **Analyzing Acceleration**:
The acceleration \( a \) of a particle in SHM is given by:
\[ a = -\omega^2 x \]
- If we take the ratio of acceleration to displacement \( \frac{a}{x} \), we get:
\[ \frac{a}{x} = -\omega^2 \]
- Here, \( -\omega^2 \) is a constant for a given motion, indicating that there is a constant ratio between acceleration and displacement.

4. **Analyzing Mass**:
Mass \( m \) is a constant property of the object and does not change with displacement. Therefore, the ratio \( \frac{x}{m} \) is not meaningful in the context of SHM, as mass does not vary with displacement.

5. **Analyzing Time Period**:
The time period \( T \) of SHM is given by:
\[ T = \frac{2\pi}{\omega} \]
- The time period is a constant for a given system and does not depend on the displacement \( x \). Hence, the ratio \( \frac{x}{T} \) is also not constant.

6. **Conclusion**:
Based on the analysis, the only quantity that maintains a constant ratio with displacement in SHM is acceleration. Therefore, the correct answer is **acceleration**.

### Final Answer:
The correct option is **acceleration**.